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117 relations: Acyclic coloring, Almost all, Aperiodic graph, Arboricity, Baranyai's theorem, Biconnected graph, Bipartite double cover, Bipartite graph, Bridge (graph theory), Brooks' theorem, Channel allocation schemes, Claude Berge, Combinatorica, Competitive analysis (online algorithm), Complete bipartite graph, Complete coloring, Complete graph, Configuration (geometry), Critical graph, Cubic graph, Cycle graph, D. R. Fulkerson, De Bruijn–Erdős theorem (graph theory), Degree (graph theory), Deterministic finite automaton, Dinitz conjecture, Directed graph, Discrete Mathematics (journal), Distributive lattice, Dual graph, Eli Upfal, Equitable coloring, Ernst Steinitz, Eulerian path, Existential theory of the reals, Fiber-optic communication, Four color theorem, Fractional coloring, Gabriel Andrew Dirac, Generalized Petersen graph, Girth (graph theory), Glossary of graph theory terms, Graph (discrete mathematics), Graph coloring, Graph drawing, Graph factorization, Graph theory, Greedy coloring, Greg Kuperberg, Hamiltonian path, ..., Handshaking lemma, Herbert Grötzsch, Hexagon, Information Processing Letters, Integer programming, Interval edge coloring, Jin Akiyama, Journal of Combinatorial Theory, K-edge-connected graph, Kempe chain, Latin square, Lexicographical order, Line graph, Linear arboricity, Linear programming, List edge-coloring, Maria Chudnovsky, Matching (graph theory), Mathematische Annalen, Mex (mathematics), Misra & Gries edge coloring algorithm, Multigraph, National Football League, NP-completeness, NP-hardness, Odd graph, Online algorithm, Open-shop scheduling, Optical fiber, Overfull graph, Parallel algorithm, Parameterized complexity, Path coloring, Paul Seymour (mathematician), Petersen graph, Planar graph, Prism (geometry), Rainbow coloring, Ramsey's theorem, Random graph, Recursion, Regular graph, Road coloring theorem, Round-robin tournament, Scheduling (production processes), Shannon multigraph, SIAM Journal on Computing, SIAM Journal on Discrete Mathematics, Snark (graph theory), Star (graph theory), Star network, Strong coloring, Strongly connected component, Synchronizing word, Three utilities problem, Thue number, Time-division multiple access, Total coloring, Tree (graph theory), Treewidth, Triangle-free graph, Triangulation (geometry), Uniquely colorable graph, Vadim G. Vizing, Vizing's theorem, Wireless network, Wireless sensor network. Expand index (67 more) »
Acyclic coloring
In graph theory, an acyclic coloring is a (proper) vertex coloring in which every 2-chromatic subgraph is acyclic.
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Almost all
In mathematics, the term "almost all" means "all but a negligible amount".
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Aperiodic graph
In the mathematical area of graph theory, a directed graph is said to be aperiodic if there is no integer k > 1 that divides the length of every cycle of the graph.
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Arboricity
The arboricity of an undirected graph is the minimum number of forests into which its edges can be partitioned.
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Baranyai's theorem
In combinatorial mathematics, Baranyai's theorem (proved by and named after Zsolt Baranyai) deals with the decompositions of complete hypergraphs.
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Biconnected graph
In graph theory, a biconnected graph is a connected and "nonseparable" graph, meaning that if any one vertex were to be removed, the graph will remain connected.
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Bipartite double cover
In graph theory, the bipartite double cover of an undirected graph G is a bipartite covering graph of G, with twice as many vertices as G. It can be constructed as the tensor product of graphs, G × K2.
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Bipartite graph
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets U and V such that every edge connects a vertex in U to one in V. Vertex sets U and V are usually called the parts of the graph.
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Bridge (graph theory)
In graph theory, a bridge, isthmus, cut-edge, or cut arc is an edge of a graph whose deletion increases its number of connected components.
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Brooks' theorem
In graph theory, Brooks' theorem states a relationship between the maximum degree of a graph and its chromatic number.
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Channel allocation schemes
In radio resource management for wireless and cellular networks, channel allocation schemes allocate bandwidth and communication channels to base stations, access points and terminal equipment.
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Claude Berge
Claude Jacques Berge (5 June 1926 – 30 June 2002) was a French mathematician, recognized as one of the modern founders of combinatorics and graph theory.
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Combinatorica
Combinatorica is an international journal of mathematics, publishing papers in the fields of combinatorics and computer science.
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Competitive analysis (online algorithm)
Competitive analysis is a method invented for analyzing online algorithms, in which the performance of an online algorithm (which must satisfy an unpredictable sequence of requests, completing each request without being able to see the future) is compared to the performance of an optimal offline algorithm that can view the sequence of requests in advance.
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Complete bipartite graph
No description.
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Complete coloring
In graph theory, complete coloring is the opposite of harmonious coloring in the sense that it is a vertex coloring in which every pair of colors appears on at least one pair of adjacent vertices.
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Complete graph
No description.
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Configuration (geometry)
In mathematics, specifically projective geometry, a configuration in the plane consists of a finite set of points, and a finite arrangement of lines, such that each point is incident to the same number of lines and each line is incident to the same number of points.
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Critical graph
In graph theory, a critical graph is a graph G in which every vertex or edge is a critical element, that is, if its deletion decreases the chromatic number of G. Such a decrement can be not more than 1 in a graph.
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Cubic graph
In the mathematical field of graph theory, a cubic graph is a graph in which all vertices have degree three.
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Cycle graph
In graph theory, a cycle graph or circular graph is a graph that consists of a single cycle, or in other words, some number of vertices connected in a closed chain.
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D. R. Fulkerson
Delbert Ray Fulkerson (August 14, 1924 – January 10, 1976) was an American mathematician who co-developed the FordNdashFulkerson algorithm, one of the most well-known algorithms to solve the maximum flow problem in networks.
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De Bruijn–Erdős theorem (graph theory)
In graph theory, the De Bruijn–Erdős theorem states that, in graph coloring for an infinite graph, the number of colors needed is the same as the largest number of colors needed by any of its finite subgraphs (if this number is finite).
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Degree (graph theory)
In graph theory, the degree (or valency) of a vertex of a graph is the number of edges incident to the vertex, with loops counted twice.
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Deterministic finite automaton
In the theory of computation, a branch of theoretical computer science, a deterministic finite automaton (DFA)—also known as a deterministic finite acceptor (DFA) and a deterministic finite state machine (DFSM) or a deterministic finite state automaton (DFSA)—is a finite-state machine that accepts or rejects strings of symbols and only produces a unique computation (or run) of the automaton for each input string.
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Dinitz conjecture
In combinatorics, the Dinitz theorem (formerly known as Dinitz conjecture) is a statement about the extension of arrays to partial Latin squares, proposed in 1979 by Jeff Dinitz, and proved in 1994 by Fred Galvin.
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Directed graph
In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is a set of vertices connected by edges, where the edges have a direction associated with them.
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Discrete Mathematics (journal)
Discrete Mathematics is a biweekly peer-reviewed scientific journal in the broad area of discrete mathematics, combinatorics, graph theory, and their applications.
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Distributive lattice
In mathematics, a distributive lattice is a lattice in which the operations of join and meet distribute over each other.
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Dual graph
In the mathematical discipline of graph theory, the dual graph of a plane graph is a graph that has a vertex for each face of.
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Eli Upfal
Eli Upfal is a computer science researcher, currently the Rush C. Hawkins Professor of Computer Science at Brown University.
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Equitable coloring
In graph theory, an area of mathematics, an equitable coloring is an assignment of colors to the vertices of an undirected graph, in such a way that.
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Ernst Steinitz
Ernst Steinitz (13 June 1871 – 29 September 1928) was a German mathematician.
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Eulerian path
In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph which visits every edge exactly once.
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Existential theory of the reals
In mathematical logic, computational complexity theory, and computer science, the existential theory of the reals is the set of all true sentences of the form where F(X_1,\dots X_n) is a quantifier-free formula involving equalities and inequalities of real polynomials.
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Fiber-optic communication
Fiber-optic communication is a method of transmitting information from one place to another by sending pulses of light through an optical fiber.
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Four color theorem
In mathematics, the four color theorem, or the four color map theorem, states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color.
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Fractional coloring
Fractional coloring is a topic in a young branch of graph theory known as fractional graph theory.
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Gabriel Andrew Dirac
Gabriel Andrew Dirac (13 March 1925 – 20 July 1984) was a mathematician who mainly worked in graph theory.
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Generalized Petersen graph
In graph theory, the generalized Petersen graphs are a family of cubic graphs formed by connecting the vertices of a regular polygon to the corresponding vertices of a star polygon.
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Girth (graph theory)
In graph theory, the girth of a graph is the length of a shortest cycle contained in the graph.
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Glossary of graph theory terms
This is a glossary of graph theory terms.
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Graph (discrete mathematics)
In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".
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Graph coloring
In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints.
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Graph drawing
Graph drawing is an area of mathematics and computer science combining methods from geometric graph theory and information visualization to derive two-dimensional depictions of graphs arising from applications such as social network analysis, cartography, linguistics, and bioinformatics.
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Graph factorization
In graph theory, a factor of a graph G is a spanning subgraph, i.e., a subgraph that has the same vertex set as G. A k-factor of a graph is a spanning k-regular subgraph, and a k-factorization partitions the edges of the graph into disjoint k-factors.
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Graph theory
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
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Greedy coloring
In the study of graph coloring problems in mathematics and computer science, a greedy coloring is a coloring of the vertices of a graph formed by a greedy algorithm that considers the vertices of the graph in sequence and assigns each vertex its first available color.
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Greg Kuperberg
Greg Kuperberg (born July 4, 1967) is a Polish-born American mathematician known for his contributions to geometric topology, quantum algebra, and combinatorics.
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Hamiltonian path
In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once.
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Handshaking lemma
In graph theory, a branch of mathematics, the handshaking lemma is the statement that every finite undirected graph has an even number of vertices with odd degree (the number of edges touching the vertex).
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Herbert Grötzsch
Camillo Herbert Grötzsch (21 May 1902 – 15 May 1993) was a German mathematician.
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Hexagon
In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon.
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Information Processing Letters
Information Processing Letters is a peer reviewed scientific journal in the field of computer science, published by Elsevier.
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Integer programming
An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers.
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Interval edge coloring
Interval edge coloring is a type of edge coloring in which edges are colored such that they form a set of intervals and each color in the interval set is at least used once to color the edges of the graph.It is to be noted that at each vertex in the graph the colors used form a consecutive set of natural numbers.
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Jin Akiyama
Jin Akiyama (秋山仁, born 1946) is a Japanese mathematician, known for his appearances on Japanese prime-time television (NHK) presenting magic tricks with mathematical explanations.
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Journal of Combinatorial Theory
The Journal of Combinatorial Theory, Series A and Series B, are mathematical journals specializing in combinatorics and related areas.
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K-edge-connected graph
In graph theory, a connected graph is k-edge-connected if it remains connected whenever fewer than k edges are removed.
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Kempe chain
In mathematics, a Kempe chain is a device used mainly in the study of the four colour theorem.
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Latin square
In combinatorics and in experimental design, a Latin square is an n × n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column.
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Lexicographical order
In mathematics, the lexicographic or lexicographical order (also known as lexical order, dictionary order, alphabetical order or lexicographic(al) product) is a generalization of the way words are alphabetically ordered based on the alphabetical order of their component letters.
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Line graph
In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. The name line graph comes from a paper by although both and used the construction before this.
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Linear arboricity
In graph theory, a branch of mathematics, the linear arboricity of an undirected graph is the smallest number of linear forests its edges can be partitioned into.
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Linear programming
Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.
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List edge-coloring
In mathematics, list edge-coloring is a type of graph coloring that combines list coloring and edge coloring.
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Maria Chudnovsky
Maria Chudnovsky (born January 6, 1977) is an Israeli-American mathematician working on graph theory and combinatorial optimization.
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Matching (graph theory)
In the mathematical discipline of graph theory, a matching or independent edge set in a graph is a set of edges without common vertices.
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Mathematische Annalen
Mathematische Annalen (abbreviated as Math. Ann. or, formerly, Math. Annal.) is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann.
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Mex (mathematics)
In mathematics, the mex of a subset of a well-ordered set is the smallest value from the whole set that does not belong to the subset.
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Misra & Gries edge coloring algorithm
The Misra & Gries edge coloring algorithm is a polynomial time algorithm in graph theory that finds an edge coloring of any graph.
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Multigraph
In mathematics, and more specifically in graph theory, a multigraph (in contrast to a simple graph) is a graph which is permitted to have multiple edges (also called parallel edges), that is, edges that have the same end nodes.
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National Football League
The National Football League (NFL) is a professional American football league consisting of 32 teams, divided equally between the National Football Conference (NFC) and the American Football Conference (AFC).
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NP-completeness
In computational complexity theory, an NP-complete decision problem is one belonging to both the NP and the NP-hard complexity classes.
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NP-hardness
NP-hardness (''n''on-deterministic ''p''olynomial-time hardness), in computational complexity theory, is the defining property of a class of problems that are, informally, "at least as hard as the hardest problems in NP".
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Odd graph
In the mathematical field of graph theory, the odd graphs On are a family of symmetric graphs with high odd girth, defined from certain set systems.
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Online algorithm
In computer science, an online algorithm is one that can process its input piece-by-piece in a serial fashion, i.e., in the order that the input is fed to the algorithm, without having the entire input available from the start.
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Open-shop scheduling
In theoretical computer science and operations research, the open-shop scheduling problem (OSSP) is a scheduling problem in which a given set of jobs must each be processed for given amounts of time at each of a given set of workstations, in an arbitrary order, and the goal is to determine the time at which each job is to be processed at each workstation.
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Optical fiber
An optical fiber or optical fibre is a flexible, transparent fiber made by drawing glass (silica) or plastic to a diameter slightly thicker than that of a human hair.
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Overfull graph
In graph theory, an overfull graph is a graph whose size is greater than the product of its maximum degree and half of its order floored, i.e. |E| > \Delta (G) \lfloor |V|/2 \rfloor where |E| is the size of G, \displaystyle\Delta(G) is the maximum degree of G, and |V| is the order of G. The concept of an overfull subgraph, an overfull graph that is a subgraph, immediately follows.
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Parallel algorithm
In computer science, a parallel algorithm, as opposed to a traditional serial algorithm, is an algorithm which can be executed a piece at a time on many different processing devices, and then combined together again at the end to get the correct result.
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Parameterized complexity
In computer science, parameterized complexity is a branch of computational complexity theory that focuses on classifying computational problems according to their inherent difficulty with respect to multiple parameters of the input or output.
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Path coloring
In graph theory, path coloring usually refers to one of two problems.
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Paul Seymour (mathematician)
Paul Seymour (born July 26, 1950) is currently a professor at Princeton University; half in the department of mathematics and half in the program in applied and computational math.
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Petersen graph
In the mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges.
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Planar graph
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints.
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Prism (geometry)
In geometry, a prism is a polyhedron comprising an n-sided polygonal base, a second base which is a translated copy (rigidly moved without rotation) of the first, and n other faces (necessarily all parallelograms) joining corresponding sides of the two bases.
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Rainbow coloring
In graph theory, a path in an edge-colored graph is said to be rainbow if no color repeats on it.
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Ramsey's theorem
In combinatorial mathematics, Ramsey's theorem states that one will find monochromatic cliques in any edge labelling (with colours) of a sufficiently large complete graph.
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Random graph
In mathematics, random graph is the general term to refer to probability distributions over graphs.
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Recursion
Recursion occurs when a thing is defined in terms of itself or of its type.
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Regular graph
In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency.
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Road coloring theorem
In graph theory the road coloring theorem, known until recently as the road coloring conjecture, deals with synchronized instructions.
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Round-robin tournament
A round-robin tournament (or all-play-all tournament) is a competition in which each contestant meets all other contestants in turn.
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Scheduling (production processes)
Scheduling is the process of arranging, controlling and optimizing work and workloads in a production process or manufacturing process.
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Shannon multigraph
In the mathematical discipline of graph theory, Shannon multigraphs, named after Claude Shannon by, are a special type of triangle graphs, which are used in the field of edge coloring in particular.
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SIAM Journal on Computing
The SIAM Journal on Computing is a scientific journal focusing on the mathematical and formal aspects of computer science.
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SIAM Journal on Discrete Mathematics
SIAM Journal on Discrete Mathematics is a peer-reviewed mathematics journal published quarterly by the Society for Industrial and Applied Mathematics (SIAM).
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Snark (graph theory)
In the mathematical field of graph theory, a snark is a simple, connected, bridgeless cubic graph with chromatic index equal to 4.
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Star (graph theory)
In graph theory, a star Sk is the complete bipartite graph K1,k: a tree with one internal node and k leaves (but, no internal nodes and k + 1 leaves when k ≤ 1).
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Star network
A Star network is one of the most common computer network topologies.
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Strong coloring
In graph theory, a strong coloring, with respect to a partition of the vertices into (disjoint) subsets of equal sizes, is a (proper) vertex coloring in which every color appears exactly once in every partition.
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Strongly connected component
In the mathematical theory of directed graphs, a graph is said to be strongly connected or diconnected if every vertex is reachable from every other vertex.
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Synchronizing word
In computer science, more precisely, in the theory of deterministic finite automata (DFA), a synchronizing word or reset sequence is a word in the input alphabet of the DFA which sends any state of the DFA to one and the same state.
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Three utilities problem
The classical mathematical puzzle known as the three utilities problem; the three cottages problem or sometimes water, gas and electricity can be stated as follows: The problem is an abstract mathematical puzzle which imposes constraints that would not exist in a practical engineering situation.
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Thue number
In the mathematical area of graph theory, the Thue number of a graph is a variation of the chromatic index, defined by Alon et al.
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Time-division multiple access
Time-division multiple access (TDMA) is a channel access method for shared-medium networks.
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Total coloring
In graph theory, total coloring is a type of graph coloring on the vertices and edges of a graph.
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Tree (graph theory)
In mathematics, and more specifically in graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path.
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Treewidth
In graph theory, the treewidth of an undirected graph is a number associated with the graph.
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Triangle-free graph
In the mathematical area of graph theory, a triangle-free graph is an undirected graph in which no three vertices form a triangle of edges.
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Triangulation (geometry)
In geometry, a triangulation is a subdivision of a planar object into triangles, and by extension the subdivision of a higher-dimension geometric object into simplices.
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Uniquely colorable graph
In graph theory, a uniquely colorable graph is a k-chromatic graph that has only one possible (proper) ''k''-coloring up to permutation of the colors.
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Vadim G. Vizing
Vadim Georgievich Vizing (Вади́м Гео́ргиевич Визинг, Вадим Георгійович Візінг; 25 March 1937 – 23 August 2017) was a Soviet and Ukrainian mathematician known for his contributions to graph theory, and especially for Vizing's theorem stating that the edges of any graph with maximum degree Δ can be colored with at most Δ + 1 colors.
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Vizing's theorem
In graph theory, Vizing's theorem (named for Vadim G. Vizing who published it in 1964) states that every simple undirected graph may be edge colored using a number of colors that is at most one larger than the maximum degree of the graph.
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Wireless network
A wireless network is a computer network that uses wireless data connections between network nodes.
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Wireless sensor network
Wireless sensor network (WSN) refers to a group of spatially dispersed and dedicated sensors for monitoring and recording the physical conditions of the environment and organizing the collected data at a central location.
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Algorithms for edge coloring, Chromatic index, Edge chromatic number, Edge colouring, K-edge colorable, Tait coloring.
References
[1] https://en.wikipedia.org/wiki/Edge_coloring
