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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' Theorem and Beyond
We collect some of our favorite proofs of Brooks' Theorem, highlighting advantages and extensions of each. The proofs illustrate… 
2014
2014
Brooks type results for conflict-free colorings and {a, b}-factors in graphs
2011
2011
A Brooks' Theorem for Triangle-Free Graphs
Let G be a triangle-free graph with maximum degree \delta(G). We show that the chromatic number \c{hi}(G) is less than 67(1 + o(1… 
2007
2007
An inequality for the group chromatic number of a graph
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… 
2002
2002
Fault tolerant distributed coloring algorithms that stabilize in linear time
We propose two new self-stabilizing distributed algorithms for proper ?+1 (?is the maximum degree of a node in the graph… 
2002
2002
A note on Brooks' theorem for triangle-free graphs
For the class of triangle-free graphs Brooks’ Theorem can be restated in terms of forbidden induced subgraphs, i.e. let G be a… 
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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