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arXiv · 1209.1176

Edge-colouring eight-regular planar graphs

Maria Chudnovsky·Katherine Edwards·Paul Seymour
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Abstract

It was conjectured by the third author in about 1973 that every $d$-regular planar graph (possibly with parallel edges) can be $d$-edge-coloured, provided that for every odd set $X$ of vertices, there are at least $d$ edges between $X$ and its complement. For $d = 3$ this is the four-colour theorem, and the conjecture has been proved for all $d\le 7$, by various authors. Here we prove it for $d = 8$.

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Maria Chudnovsky, Katherine Edwards, Paul Seymour. 2012-09-06. Edge-colouring eight-regular planar graphs. https://arxiv.org/abs/1209.1176

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