Edge-disjoint Hamilton cycles in graphs

Authors:
Demetres Christofides;Daniela KüHn;Deryk Osthus
Affiliations:
School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London, E1 4NS, UK;School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK;School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK
Venue:
Journal of Combinatorial Theory Series B
Year:
2012

Citing 2
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Abstract

In this paper we give an approximate answer to a question of Nash-Williams from 1970: we show that for every @a0, every sufficiently large graph on n vertices with minimum degree at least (1/2+@a)n contains at least n/8 edge-disjoint Hamilton cycles. More generally, we give an asymptotically best possible answer for the number of edge-disjoint Hamilton cycles that a graph G with minimum degree @d must have. We also prove an approximate version of another long-standing conjecture of Nash-Williams: we show that for every @a0, every (almost) regular and sufficiently large graph on n vertices with minimum degree at least (1/2+@a)n can be almost decomposed into edge-disjoint Hamilton cycles.