Annals of Combinatorics

, Volume 13, Issue 4, pp 403–412

Small Spectral Gap in the Combinatorial Laplacian Implies Hamiltonian

Open Access


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



Hamiltonian combinatorial Laplacian spectral graph theory 


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Copyright information

© The Author(s) 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA
  2. 2.Department of MathematicsUniversity of CaliforniaSan Diego, La JollaUSA

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