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76 relations: Abstract simplicial complex, Algorithm, Automatic test pattern generation, Biclustering, Biconnected component, Bioinformatics, Bipartite dimension, Block graph, Bron–Kerbosch algorithm, Chemical database, Chemistry, Chordal graph, Clique, Clique complex, Clique cover, Clique graph, Clique problem, Clique-sum, Clique-width, Cluster graph, Cograph, Complement graph, Complete bipartite graph, Complete graph, Computer science, Connected component (graph theory), Dense graph, Ecological niche, Electrical engineering, Erdős–Faber–Lovász conjecture, Food chain, Gene expression, Graph (discrete mathematics), Graph coloring, Graph minor, Graph theory, Hadwiger conjecture (graph theory), Hadwiger number, Hardness of approximation, Homeomorphism (graph theory), Independent set (graph theory), Induced subgraph, Intersection graph, Intersection number (graph theory), Interval graph, Karp's 21 NP-complete problems, Kuratowski's theorem, Line graph, Mathematics, Maximal independent set, ..., Median algebra, Median graph, Neighbourhood (graph theory), NP-completeness, Parameterized complexity, Perfect graph, Perfect phylogeny, Phylogenetic tree, Planar graph, Power graph analysis, Proceedings of the IEEE, Proceedings of the National Academy of Sciences of the United States of America, Protein structure prediction, Protein–protein interaction, Ramsey theory, Ramsey's theorem, Simplex graph, Social network, Split graph, Time complexity, Triangle-free graph, Turán graph, Turán's theorem, Upper and lower bounds, Vertex (graph theory), Wagner's theorem. Expand index (26 more) »
Abstract simplicial complex
In mathematics, an abstract simplicial complex is a purely combinatorial description of the geometric notion of a simplicial complex, consisting of a family of non-empty finite sets closed under the operation of taking non-empty subsets.
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Algorithm
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.
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Automatic test pattern generation
ATPG (acronym for both Automatic Test Pattern Generation and Automatic Test Pattern Generator) is an electronic design automation method/technology used to find an input (or test) sequence that, when applied to a digital circuit, enables automatic test equipment to distinguish between the correct circuit behavior and the faulty circuit behavior caused by defects.
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Biclustering
Biclustering, block clustering, co-clustering, or two-mode clustering is a data mining technique which allows simultaneous clustering of the rows and columns of a matrix.
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Biconnected component
In graph theory, a biconnected component (also known as a block or 2-connected component) is a maximal biconnected subgraph.
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Bioinformatics
Bioinformatics is an interdisciplinary field that develops methods and software tools for understanding biological data.
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Bipartite dimension
In the mathematical fields of graph theory and combinatorial optimization, the bipartite dimension or biclique cover number of a graph G.
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Block graph
In graph theory, a branch of combinatorial mathematics, a block graph or clique tree.
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Bron–Kerbosch algorithm
In computer science, the Bron–Kerbosch algorithm is an algorithm for finding maximal cliques in an undirected graph.
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Chemical database
A chemical database is a database specifically designed to store chemical information.
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Chemistry
Chemistry is the scientific discipline involved with compounds composed of atoms, i.e. elements, and molecules, i.e. combinations of atoms: their composition, structure, properties, behavior and the changes they undergo during a reaction with other compounds.
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Chordal graph
In the mathematical area of graph theory, a chordal graph is one in which all cycles of four or more vertices have a chord, which is an edge that is not part of the cycle but connects two vertices of the cycle.
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Clique
A clique (AusE, CanE, or), in the social sciences, is a group of individuals who interact with one another and share similar interests.
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Clique complex
Clique complexes, flag complexes, and conformal hypergraphs are closely related mathematical objects in graph theory and geometric topology that each describe the cliques (complete subgraphs) of an undirected graph.
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Clique cover
In graph theory, a clique cover or partition into cliques of a given undirected graph is a partition of the vertices of the graph into cliques, subsets of vertices within which every two vertices are adjacent.
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Clique graph
In graph theory, a clique graph of an undirected graph G is another graph K(G) that represents the structure of cliques in G. Clique graphs were discussed at least as early as 1968, and a characterization of clique graphs was given in 1971.
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Clique problem
In computer science, the clique problem is the computational problem of finding cliques (subsets of vertices, all adjacent to each other, also called complete subgraphs) in a graph.
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Clique-sum
In graph theory, a branch of mathematics, a clique-sum is a way of combining two graphs by gluing them together at a clique, analogous to the connected sum operation in topology.
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Clique-width
In graph theory, the clique-width of a graph G is a parameter that describes the structural complexity of the graph; it is closely related to treewidth, but unlike treewidth it can be bounded even for dense graphs.
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Cluster graph
In graph theory, a branch of mathematics, a cluster graph is a graph formed from the disjoint union of complete graphs.
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Cograph
In graph theory, a cograph, or complement-reducible graph, or P4-free graph, is a graph that can be generated from the single-vertex graph K1 by complementation and disjoint union.
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Complement graph
In graph theory, the complement or inverse of a graph is a graph on the same vertices such that two distinct vertices of are adjacent if and only if they are not adjacent in.
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Complete bipartite graph
No description.
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Complete graph
No description.
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Computer science
Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.
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Connected component (graph theory)
In graph theory, a connected component (or just component) of an undirected graph is a subgraph in which any two vertices are connected to each other by paths, and which is connected to no additional vertices in the supergraph.
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Dense graph
In mathematics, a dense graph is a graph in which the number of edges is close to the maximal number of edges.
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Ecological niche
In ecology, a niche (CanE, or) is the fit of a species living under specific environmental conditions.
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Electrical engineering
Electrical engineering is a professional engineering discipline that generally deals with the study and application of electricity, electronics, and electromagnetism.
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Erdős–Faber–Lovász conjecture
In graph theory, the Erdős–Faber–Lovász conjecture is an unsolved problem about graph coloring, named after Paul Erdős, Vance Faber, and László Lovász, who formulated it in 1972.
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Food chain
A food chain is a linear network of links in a food web starting from producer organisms (such as grass or trees which use radiation from the Sun to make their food) and ending at apex predator species (like grizzly bears or killer whales), detritivores (like earthworms or woodlice), or decomposer species (such as fungi or bacteria).
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Gene expression
Gene expression is the process by which information from a gene is used in the synthesis of a functional gene product.
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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 minor
In graph theory, an undirected graph H is called a minor of the graph G if H can be formed from G by deleting edges and vertices and by contracting edges.
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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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Hadwiger conjecture (graph theory)
In graph theory, the Hadwiger conjecture (or Hadwiger's conjecture) states that, if all proper colorings of an undirected graph G use k or more colors, then one can find k disjoint connected subgraphs of G such that each subgraph is connected by an edge to each other subgraph.
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Hadwiger number
In graph theory, the Hadwiger number of an undirected graph G is the size of the largest complete graph that can be obtained by contracting edges of G. Equivalently, the Hadwiger number h(G) is the largest number k for which the complete graph Kk is a minor of G, a smaller graph obtained from G by edge contractions and vertex and edge deletions.
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Hardness of approximation
In computer science, hardness of approximation is a field that studies the algorithmic complexity of finding near-optimal solutions to optimization problems.
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Homeomorphism (graph theory)
In graph theory, two graphs G and G' are homeomorphic if there is a graph isomorphism from some subdivision of G to some subdivision of G'.
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Independent set (graph theory)
In graph theory, an independent set or stable set is a set of vertices in a graph, no two of which are adjacent.
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Induced subgraph
In graph theory, an induced subgraph of a graph is another graph, formed from a subset of the vertices of the graph and all of the edges connecting pairs of vertices in that subset.
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Intersection graph
In the mathematical area of graph theory, an intersection graph is a graph that represents the pattern of intersections of a family of sets.
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Intersection number (graph theory)
In the mathematical field of graph theory, the intersection number of a graph is the smallest number of elements in a representation of as an intersection graph of finite sets.
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Interval graph
In graph theory, an interval graph is the intersection graph of a family of intervals on the real line.
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Karp's 21 NP-complete problems
In computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete.
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Kuratowski's theorem
In graph theory, Kuratowski's theorem is a mathematical forbidden graph characterization of planar graphs, named after Kazimierz Kuratowski.
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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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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Maximal independent set
In graph theory, a maximal independent set (MIS) or maximal stable set is an independent set that is not a subset of any other independent set.
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Median algebra
In mathematics, a median algebra is a set with a ternary operation \langle x,y,z \rangle satisfying a set of axioms which generalise the notion of median or majority function, as a Boolean function.
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Median graph
In graph theory, a division of mathematics, a median graph is an undirected graph in which every three vertices a, b, and c have a unique median: a vertex m(a,b,c) that belongs to shortest paths between each pair of a, b, and c. The concept of median graphs has long been studied, for instance by or (more explicitly) by, but the first paper to call them "median graphs" appears to be.
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Neighbourhood (graph theory)
In graph theory, an adjacent vertex of a vertex v in a graph is a vertex that is connected to v by an edge.
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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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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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Perfect graph
In graph theory, a perfect graph is a graph in which the chromatic number of every induced subgraph equals the size of the largest clique of that subgraph.
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Perfect phylogeny
Perfect phylogeny is a term used in computational phylogenetics to denote a phylogenetic tree in which all internal nodes may be labeled such that all characters evolve down the tree without homoplasy.
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Phylogenetic tree
A phylogenetic tree or evolutionary tree is a branching diagram or "tree" showing the evolutionary relationships among various biological species or other entities—their phylogeny—based upon similarities and differences in their physical or genetic characteristics.
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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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Power graph analysis
In computational biology, power graph analysis is a method for the analysis and representation of complex networks.
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Proceedings of the IEEE
The Proceedings of the IEEE is a monthly peer-reviewed scientific journal published by the Institute of Electrical and Electronics Engineers (IEEE).
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Proceedings of the National Academy of Sciences of the United States of America
Proceedings of the National Academy of Sciences of the United States of America (PNAS) is the official scientific journal of the National Academy of Sciences, published since 1915.
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Protein structure prediction
Protein structure prediction is the inference of the three-dimensional structure of a protein from its amino acid sequence—that is, the prediction of its folding and its secondary and tertiary structure from its primary structure.
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Protein–protein interaction
Protein–protein interactions (PPIs) are the physical contacts of high specificity established between two or more protein molecules as a result of biochemical events steered by electrostatic forces including the hydrophobic effect.
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Ramsey theory
Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that studies the conditions under which order must appear.
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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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Simplex graph
In graph theory, a branch of mathematics, the simplex graph κ(G) of an undirected graph G is itself a graph, with one node for each clique (a set of mutually adjacent vertices) in G. Two nodes of κ(G) are linked by an edge whenever the corresponding two cliques differ in the presence or absence of a single vertex.
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Social network
A social network is a social structure made up of a set of social actors (such as individuals or organizations), sets of dyadic ties, and other social interactions between actors.
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Split graph
In graph theory, a branch of mathematics, a split graph is a graph in which the vertices can be partitioned into a clique and an independent set.
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Time complexity
In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.
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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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Turán graph
No description.
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Turán's theorem
In graph theory, Turán's theorem is a result on the number of edges in a ''K''''r''+1-free graph.
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Upper and lower bounds
In mathematics, especially in order theory, an upper bound of a subset S of some partially ordered set (K, ≤) is an element of K which is greater than or equal to every element of S. The term lower bound is defined dually as an element of K which is less than or equal to every element of S. A set with an upper bound is said to be bounded from above by that bound, a set with a lower bound is said to be bounded from below by that bound.
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Vertex (graph theory)
In mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices).
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Wagner's theorem
In graph theory, Wagner's theorem is a mathematical forbidden graph characterization of planar graphs, named after Klaus Wagner, stating that a finite graph is planar if and only if its minors include neither K5 (the complete graph on five vertices) nor K3,3 (the utility graph, a complete bipartite graph on six vertices).
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Clique number, K-clique, Maximal clique, Maximum clique.
References
[1] https://en.wikipedia.org/wiki/Clique_(graph_theory)
