Skip to main content

Edge-colouring seven-regular planar graphs

Author(s): Chudnovsky, Maria; Edwards, Katherine; Kawarabayashi, Ken-ichi; Seymour, Paul

Download
To refer to this page use: http://arks.princeton.edu/ark:/88435/pr19g71
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.
Publication Date: Nov-2015
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.
DOI: http://dx.doi.org/10.1016/j.jctb.2014.11.005
Pages: 276-302
Type of Material: Journal Article
Journal/Proceeding Title: Journal of combinatorial theory. Series B.
Version: Author's manuscript



Items in OAR@Princeton are protected by copyright, with all rights reserved, unless otherwise indicated.