Hamilton cycles in highly connected and expanding graphs

Details Hamilton cycles in highly connected and expanding graphs Hamilton cycles in highly connected and expanding graphs

2006-12-24

arxiv.org/abs/math/0612751v1

Mathematics

Combinatorics

19 pages

Scientific paper

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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