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A Stronger Bound for the Strong Chromatic Index

Published online by Cambridge University Press:  19 July 2017

HENNING BRUHN  and
FELIX JOOS
HENNING BRUHN
Affiliation:
Institut für Optimierung und Operations Research, Universität Ulm, Ulm, Germany (e-mail: henning.bruhn@uni-ulm.de, felix.joos@uni-ulm.de)
FELIX JOOS
Affiliation:
Institut für Optimierung und Operations Research, Universität Ulm, Ulm, Germany (e-mail: henning.bruhn@uni-ulm.de, felix.joos@uni-ulm.de)
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Abstract

We prove χ′s (G) ≤ 1.93 Δ(G)2 for graphs of sufficiently large maximum degree where χ′s (G) is the strong chromatic index of G. This improves an old bound of Molloy and Reed. As a by-product, we present a Talagrand-type inequality where we are allowed to exclude unlikely bad outcomes that would otherwise render the inequality unusable.

Keywords

05C15

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 27 , Issue 1 , January 2018 , pp. 21 - 43
Copyright
Copyright © Cambridge University Press 2017 

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