Annals of Combinatorics

, Volume 13, Issue 4, pp 403–412

Small Spectral Gap in the Combinatorial Laplacian Implies Hamiltonian

Authors

    • Department of MathematicsUniversity of California
  • Fan Chung
    • Department of MathematicsUniversity of California
Open AccessArticle

DOI: 10.1007/s00026-009-0039-4

Cite this article as:
Butler, S. & Chung, F. Ann. Comb. (2010) 13: 403. doi:10.1007/s00026-009-0039-4

Abstract

We consider the spectral and algorithmic aspects of the problem of finding a Hamiltonian cycle in a graph. We show that a sufficient condition for a graph being Hamiltonian is that the nontrivial eigenvalues of the combinatorial Laplacian are sufficiently close to the average degree of the graph. An algorithm is given for the problem of finding a Hamiltonian cycle in graphs with bounded spectral gaps which has complexity of order ncln n.

AMS Subject Classification

05C45

Keywords

Hamiltoniancombinatorial Laplacianspectral graph theory
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© The Author(s) 2009