Mathematics – Combinatorics
Scientific paper
2012-03-17
Mathematics
Combinatorics
Scientific paper
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 G_n,p a.a.s. has size \lfloor delta(G_n,p) /2 \rfloor. Glebov, Krivelevich and Szab\'o 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^{117}n / n < p < 1-n^{-1/8}, a.a.s. the edges of G_n,p can be covered by \lceil Delta(G_n,p)/2 \rceil Hamilton cycles. This is clearly optimal and improves an approximate result of Glebov, Krivelevich and Szab\'o, which holds for p > n^{-1+\eps}. Our proof is based on a result of Knox, K\"uhn and Osthus on packing Hamilton cycles in pseudorandom graphs.
Hefetz Dan
Kühn Daniela
Lapinskas John
Osthus Deryk
No associations
LandOfFree
Optimal covers with Hamilton cycles in random graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Optimal covers with Hamilton cycles in random graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Optimal covers with Hamilton cycles in random graphs will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-313114