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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.
2018
2018
A short proof of Brooks' theorem
We give a simple short proof of Brooks' theorem using only induction and greedy coloring, while avoiding issues of graph… 
2015
2015
A Brooks‐Type Theorem for the Bichromatic Number
A classical theorem of Brooks in graph coloring theory states that every connected graph G has its chromatic number χ(G) less… 
2014
2014
No Quantum Brooks' Theorem
First, I introduce quantum graph theory. I also discuss a known lower bound on the independence numbers and derive from it an… 
2012
2012
New Descriptions of the Lovász Number, and the Weak Sandwich Theorem
In 1979, L. Lovasz introduced the concept of an orthonormalrepresentation of a graph, and also a related value, now popularly… 
2011
2011
A Strengthening of Brooks' Theorem for Line Graphs
We prove that if $G$ is the line graph of a multigraph, then the chromatic number $\chi(G)$ of $G$ is at most $\max\left\{\omega… 
2010
2010
Edge-choosability of cubic graphs and the polynomial method
A graph is k-edge-choosable if for any assignment of a list of at least k colours to each edge, there is a proper edge-colouring… 
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
A List Version of Dirac's Theorem on the Number of Edges in Colour-critical Graphs
One of the basic results in graph colouring is Brooks' theorem [R. 
1995
1995
Degree-bounded coloring of graphs: Variations on a theme by brooks
A graph G is degree-bounded-colorable (briefly, db-colorable) if it can be properly vertex-colored with colors 1,2, …, k ≤ Δ(G… 
1977
1977
An extension of Brooks' theorem to n-degenerate graphs
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