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Brooks' theorem

Index Brooks' theorem

In graph theory, Brooks' theorem states a relationship between the maximum degree of a graph and its chromatic number. [1]

27 relations: Biconnected graph, Clique (graph theory), Combinatorica, Complete graph, Connectivity (graph theory), Cycle graph, Degree (graph theory), Dense graph, Edge coloring, Equitable coloring, Graph (discrete mathematics), Graph coloring, Graph theory, Greedy coloring, Information Processing Letters, Journal of Combinatorial Theory, List coloring, Mathematical Proceedings of the Cambridge Philosophical Society, Mehdi Behzad, Neighbourhood (graph theory), R. Leonard Brooks, Regular graph, SIAM Journal on Discrete Mathematics, Spanning tree, Total coloring, Triangle-free graph, Vizing's theorem.

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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Clique (graph theory)

In the mathematical area of graph theory, a clique is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent; that is, its induced subgraph is complete.

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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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Complete graph

No description.

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Connectivity (graph theory)

In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to disconnect the remaining nodes from each other.

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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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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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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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Edge coloring

In graph theory, an edge coloring of a graph is an assignment of "colors" to the edges of the graph so that no two adjacent edges have the same color.

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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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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 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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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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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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List coloring

In graph theory, a branch of mathematics, list coloring is a type of graph coloring where each vertex can be restricted to a list of allowed colors.

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Mathematical Proceedings of the Cambridge Philosophical Society

Mathematical Proceedings of the Cambridge Philosophical Society is a mathematical journal published by Cambridge University Press for the Cambridge Philosophical Society.

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Mehdi Behzad

Mehdi Behzad (Persian:مهدی بهزاد; born April 22, 1936) is an Iranian mathematician specializing in graph theory.

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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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R. Leonard Brooks

Rowland Leonard Brooks (February 6, 1916 – June 18, 1993), squaring.net, retrieved 2010-07-30.

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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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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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Spanning tree

In the mathematical field of graph theory, a spanning tree T of an undirected graph G is a subgraph that is a tree which includes all of the vertices of G, with minimum possible number of edges.

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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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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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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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Brooks's theorem, Brooks’ theorem.

References

[1] https://en.wikipedia.org/wiki/Brooks'_theorem

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