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Small spectral gap in the combinatorial Laplacian implies Hamiltonian. (English) Zbl 1229.05193
Summary: 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 $n^{c\ln n}$.

05C45Eulerian and Hamiltonian graphs
05C50Graphs and linear algebra
05C85Graph algorithms (graph theory)
Full Text: DOI
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