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arxiv: 1504.02583 · v1 · pith:3WSVB53Nnew · submitted 2015-04-10 · 🧮 math.CO · cs.DM· math.PR

A stronger bound for the strong chromatic index

Henning Bruhn , Felix Joos This is my paper
classification 🧮 math.CO cs.DMmath.PR
keywords boundchromaticindexinequalitystrongallowedby-productdegree
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We prove $\chi_s'(G)\leq 1.93 \Delta(G)^2$ for graphs of sufficiently large maximum degree where $\chi_s'(G)$ 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 it is allowed to exclude unlikely bad outcomes that would otherwise render the inequality unusable.

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