Three-edge-colouring doublecross cubic graphs

详细信息    查看全文

• 作者：Katherine Edwards^a ; ¹ ; Daniel P. Sanders^b ; ² ; Paul Seymour^a ; ³ ; ^{pds@math.princeton.edu" class="auth_mail" title="E-mail the corresponding author} ; Robin Thomas^c ; ⁴
• 关键词：Edge-colouring ; Petersen minor ; Four-colour theorem
• 刊名：Journal of Combinatorial Theory, Series B
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：119
• 期：Complete
• 页码：66-95
• 全文大小：635 K

文摘

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  and . 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].