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Brooks' theorem

Known as: Brooks’ theorem 
In graph theory, Brooks' theorem states a relationship between the maximum degree of a graph and its chromatic number. According to the theorem, in a… 
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Related topics

Related topics

16 relations
1-planar graphBiconnected graphClique (graph theory)Critical graph

Broader (1)

Graph coloring

Papers overview

Semantic Scholar uses AI to extract papers important to this topic.
2014
2014
A Reconfigurations Analogue of Brooks' Theorem and Its Consequences
Let G be a simple undirected connected graph on n vertices with maximum degree Δ. Brooks' Theorem states that G has a proper… 
2014
2014
Brooks type results for conflict-free colorings and {a, b}-factors in graphs
2014
2014
Brooks' Theorem and Beyond
We collect some of our favorite proofs of Brooks' Theorem, highlighting advantages and extensions of each. The proofs illustrate… 
2007
2007
An inequality for the group chromatic number of a graph
Review
2006
Review
2006
Color-Critical Graphs and Hypergraphs with Few Edges: A Survey
The current situation with bounds on the smallest number of edges in color-critical graphs and hypergraphs is discussed. 
2005
2005
Precoloring Extensions of Brooks' Theorem
Let G be a connected graph with maximum degree k (other than a complete graph or odd cycle), let W be a precolored set of… 
Highly Cited
1999
Highly Cited
1999
A Strengthening of Brooks' Theorem
  • B. Reed
  • Journal of combinatorial theory. Series B (Print)
  • 1999
  • Corpus ID: 1557604
We show that for sufficiently large ?, any graph with maximum degree at most ? and no cliques of size ? has a ??1 colouring 
Highly Cited
1995
Highly Cited
1995
On Brooks' Theorem for Sparse Graphs
Let G be a graph with maximum degree Δ(G). In this paper we prove that if the girth g(G) of G is greater than 4 then its… 
1978
1978
Another bound on the chromatic number of a graph
Highly Cited
1977
Highly Cited
1977
On an upper bound of a graph's chromatic number, depending on the graph's degree and density
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