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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

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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… 
2016
2016
SYLLABUS FOR GRADUATE COMBINATORICS 6501 (1) Enumerative Combinatorics: Bijective methods, Generating functions, Basic results in Algebraic Combinatorics, [7, 10]. (2) Graph Theory: Menger’s theorem…
  • 2016
  • Corpus ID: 40676976
(1) Enumerative Combinatorics: Bijective methods, Generating functions, Basic results in Algebraic Combinatorics, [7, 10]. (2… 
2015
2015
COLOURINGS OF m-EDGE-COLOURED GRAPHS AND SWITCHING
Graphs with m disjoint edge sets are considered, both in the presence of a switching operation and without one. The operation of… 
2013
2013
Approximation Algorithms for Bandwidth Consecutive Multicolorings - (Extended Abstract)
Let G be a graph in which each vertex v has a positive integer weight b(v) and each edge (v,w) has a nonnegative integer weight b… 
2013
2013
C O ] 1 6 M ay 2 01 3 Graphs with χ = ∆ have big cliques
Brooks’ Theorem states that if a graph has ∆ ≥ 3 and ω ≤ ∆, then χ ≤ ∆. Borodin and Kostochka conjectured that if ∆ ≥ 9 and… 
2012
2012
N ov 2 01 2 A short proof that χ can be bounded ǫ away from ∆ + 1 towards ω
In 1998 the second author proved that there is an ǫ > 0 such that every graph satisfies χ ≤ ⌈(1 − ǫ)(∆ + 1) + ǫω⌉. The first… 
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… 
2011
2011
AN IMPROVEMENT ON BROOKS ’ THEOREM 3
We prove that χ(G) ≤ max { ω(G),∆2(G), 5 6 (∆(G) + 1) } for every graph G with ∆(G) ≥ 3. Here ∆2 is the parameter introduced by… 
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… 
1992
1992
A Generalization of Brooks' Theorem