Hamilton cycles in highly connected and expanding graphs

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 two properties only: 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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Correspondence to Dan Hefetz.

Additional information

This paper is a part of the author’s Ph.D. thesis written under the supervision of Prof. Michael Krivelevich.

Research supported in part by a USA-Israel BSF grant and a grant from the Israel Science Foundation.

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Hefetz, D., Krivelevich, M. & Szabó, T. Hamilton cycles in highly connected and expanding graphs. Combinatorica 29, 547–568 (2009). https://doi.org/10.1007/s00493-009-2362-0

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Mathematics Subject Classification (2000)

  • 05C45
  • 05C40
  • 05C80
  • 05C35