Abstract
A packing of a graph G with Hamilton cycles is a set of edge-disjoint Hamilton cycles in G. Such packings have been studied intensively and recent results imply that a largest packing of Hamilton cycles in Gn,p a.a.s. has size {box drawings light up and right}δ(Gn,p)/2{box drawings light up and left}. Glebov, Krivelevich and Szabó recently initiated research on the 'dual' problem, where one asks for a set of Hamilton cycles covering all edges of G. Our main result states that for log (Formula presented.), a.a.s. the edges of Gn,p can be covered by {box drawings light up and left}{increment}(Gn,p)/2{box drawings light up and left} Hamilton cycles. This is clearly optimal and improves an approximate result of Glebov, Krivelevich and Szabó, which holds for p ≤ n-1+ε. Our proof is based on a result of Knox, Kühn and Osthus on packing Hamilton cycles in pseudorandom graphs.
Original language | English |
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Pages (from-to) | 573–596 |
Journal | Combinatorica |
Volume | 34 |
Issue number | 5 |
Early online date | 23 Jun 2014 |
DOIs | |
Publication status | Published - Oct 2014 |
ASJC Scopus subject areas
- Computational Mathematics
- Discrete Mathematics and Combinatorics