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.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Butler, S., Chung, F. Small Spectral Gap in the Combinatorial Laplacian Implies Hamiltonian. Ann. Comb. 13, 403–412 (2010). https://doi.org/10.1007/s00026-009-0039-4
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DOI: https://doi.org/10.1007/s00026-009-0039-4