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Three-edge-colouring doublecross cubic graphs

Author(s): Edwards, Katherine; Sanders, Daniel P; Seymour, Paul D; Thomas, Robin

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Abstract: A graph is apex if there is a vertex whose deletion makes the graph planar, and doublecross if it can be drawn in the plane with only two crossings, both incident with the infinite region in the natural sense. In 1966, Tutte [9] conjectured that every two-edge-connected cubic graph with no Petersen graph minor is three-edge-colourable. With Neil Robertson, two of us showed that this is true in general if it is true for apex graphs and doublecross graphs [6,7]. In another paper [8], two of us solved the apex case, but the doublecross case remained open. Here we solve the doublecross case; that is, we prove that every two-edge-connected doublecross cubic graph is three edge-colourable. The proof method is a variant on the proof of the four-colour theorem given in [5]. (C) 2015 Elsevier Inc. All rights reserved.
Publication Date: Jul-2016
Electronic Publication Date: 5-Jan-2016
Citation: Edwards, Katherine, Sanders, Daniel P, Seymour, Paul, Thomas, Robin. (2016). Three-edge-colouring doublecross cubic graphs. JOURNAL OF COMBINATORIAL THEORY SERIES B, 119 (66 - 95. doi:10.1016/j.jctb.2015.12.006
DOI: doi:10.1016/j.jctb.2015.12.006
ISSN: 0095-8956
EISSN: 1096-0902
Pages: 66 - 95
Type of Material: Journal Article
Version: Author's manuscript

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