, Volume 13, Issue 4, pp 403-412,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 12 Jan 2010

Small Spectral Gap in the Combinatorial Laplacian Implies Hamiltonian

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 n cln n .