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arXiv · 1111.3325

On covering expander graphs by Hamilton cycles

Roman Glebov·Michael Krivelevich·Tibor Szabó
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Abstract

The problem of packing Hamilton cycles in random and pseudorandom graphs has been studied extensively. In this paper, we look at the dual question of covering all edges of a graph by Hamilton cycles and prove that if a graph with maximum degree $Δ$ satisfies some basic expansion properties and contains a family of $(1-o(1))Δ/2$ edge disjoint Hamilton cycles, then there also exists a covering of its edges by $(1+o(1))Δ/2$ Hamilton cycles. This implies that for every $α>0$ and every $p \geq n^{α-1}$ there exists a covering of all edges of $G(n,p)$ by $(1+o(1))np/2$ Hamilton cycles asymptotically almost surely, which is nearly optimal.

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Roman Glebov, Michael Krivelevich, Tibor Szabó. 2011-11-14. On covering expander graphs by Hamilton cycles. https://arxiv.org/abs/1111.3325

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