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|Abstract:||A conjecture due to the fourth author states that every $d$-regular planar multigraph 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 $d\le 8$, by various authors. In particular, two of us proved it when $d=7$; and then three of us proved it when $d=8$. The methods used for the latter give a proof in the $d=7$ case that is simpler than the original, and we present it here.|
|Electronic Publication Date:||9-Jun-2015|
|Citation:||M. Chudnovsky, K. Edwards, K. Kawarabayashi, P. Seymour, Edge-colouring seven-regular planar graphs, J. Combin. Theory Ser. B 115 (2015) 276–302.|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||Journal of combinatorial theory. Series B.|
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