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The average degree of an edge-chromatic critical graph II

✍ Scribed by Douglas R. Woodall

Publisher: John Wiley and Sons
Year: 2007
Tongue: English
Weight: 224 KB
Volume: 56
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20259

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✦ Synopsis

Abstract

A graph G with maximum degree Δ and edge chromatic number $\chi\prime({G}) > \Delta$ is edge‐Δ‐critical if $\chi\prime{(G-e)} = \Delta$ for every edge e of G. It is proved that the average degree of an edge‐Δ‐critical graph is at least ${2\over 3}{(\Delta+1)}$ if $\Delta \geq 2$, at least ${2\over 3}\Delta + 1$ if $\Delta \geq 8$, and at least ${2\over 3}(\Delta + 2)$ if $\Delta \geq 15$. For large Δ, this improves on the best bound previously known, which was roughly ${1\over 2}(\Delta+\sqrt{2\Delta})$. © Wiley Periodicals, Inc. J. Graph Theory 56: 194–218, 2007

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