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Hamilton cycles in highly connected and expanding graphs

Dan Hefetz·Michael Krivelevich·Tibor Szabo
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Abstract

In this paper we prove a sufficient condition for the existence of a Hamilton cycle, which is applicable to a wide variety of graphs, including relatively sparse graphs. In contrast to previous criteria, ours is based on only two properties: one requiring expansion of ``small'' sets, the other ensuring the existence of an edge between any two disjoint ``large'' sets. We also discuss applications in positional games, random graphs and extremal graph theory.

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Dan Hefetz, Michael Krivelevich, Tibor Szabo. 2006-12-24. Hamilton cycles in highly connected and expanding graphs. https://arxiv.org/abs/math/0612751

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