Solution to a problem of Bollob\'as and H\"aggkvist on Hamilton cycles in regular graphs

Daniela Kühn; Allan Lo; Deryk Osthus; Katherine Staden

Solution to a problem of Bollob\'as and H\"aggkvist on Hamilton cycles in regular graphs

Combinatorics 2016-02-08 v2

Authors: Daniela Kühn , Allan Lo , Deryk Osthus , Katherine Staden

Abstract

We prove that, for large $n$ , every $3$ -connected $D$ -regular graph on $n$ vertices with $D \geq n/4$ is Hamiltonian. This is best possible and confirms a conjecture posed independently by Bollob\'as and H\"aggkvist in the 1970s. The proof builds on a structural decomposition result proved recently by the same authors.

Keywords

hamilton cycles regular graphs connectivity bollobás-häggkvist conjecture structural decomposition graph theory

Cite

@article{arxiv.1402.4754,
  title  = {Solution to a problem of Bollob\'as and H\"aggkvist on Hamilton cycles in regular graphs},
  author = {Daniela Kühn and Allan Lo and Deryk Osthus and Katherine Staden},
  journal= {arXiv preprint arXiv:1402.4754},
  year   = {2016}
}

Comments

42 pages, to appear in JCTB

Solution to a problem of Bollob\'as and H\"aggkvist on Hamilton cycles in regular graphs

Abstract

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