Solution to a problem of Bollobás and Häggkvist on Hamilton cycles in regular graphs

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• 作者：Daniela Kü ; hn^a ; ^{d.kuhn@bham.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Allan Lo^a ; ^{s.a.lo@bham.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Deryk Osthus^a ; ^{d.osthus@bham.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Katherine Staden^b ; ^{k.l.staden@warwick.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Hamilton cycles ; Connectivity ; Robust expansion ; Regular graphs
• 刊名：Journal of Combinatorial Theory, Series B
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：121
• 期：Complete
• 页码：85-145
• 全文大小：1020 K

文摘

We prove that, for large n, every 3-connected D-regular graph on n   vertices with class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0095895615001380&_mathId=si1.gif&_user=111111111&_pii=S0095895615001380&_rdoc=1&_issn=00958956&md5=b3101202308de778224f4c70a7242a43" title="Click to view the MathML source">D≥n/4class="mathContainer hidden">class="mathCode">$D\ge n/4$ is Hamiltonian. This is best possible and verifies the only remaining case of a conjecture posed independently by Bollobás and Häggkvist in the 1970s. The proof builds on a structural decomposition result proved recently by the same authors.