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A different short proof of Brook's theorem

A different short proof of Brooks' theorem
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2014Embargo end date: 01 Jan 2012 English Publisher:University of Zielona Góra, PolandJournal:Discussiones Mathematicae Graph Theory, volume 34, page 633 (issn: 1234-3099, eissn: 2083-5892, Copyright policy )
Authors: Rabern Landon;

doi: 10.7151/dmgt.1721 , 10.48550/arxiv.1205.3253

arXiv: 1205.3253

A different short proof of Brook's theorem

Abstract

Lov��sz gave a short proof of Brooks' theorem by coloring greedily in a good order. We give a different short proof by reducing to the cubic case. Then we show how to extend the result to (online) list coloring via the Kernel Lemma.

added cute Kernel Lemma trick to lift up to (online) list coloring

Related Organizations
Keywords

Extremal problems in graph theory, maximum degree, Vertex degrees, clique number, Coloring of graphs and hypergraphs, QA1-939, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Mathematics, coloring

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
5
Average
Top 10%
Average
Green
Published in a Diamond OA journal