Random Structures & Algorithms
Local resilience and hamiltonicity maker–breaker games in random regular graphs
Combinatorics, Probability and Computing
Expanders are universal for the class of all spanning trees
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Packing tight Hamilton cycles in 3-uniform hypergraphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A survey on Hamilton cycles in directed graphs
European Journal of Combinatorics
Packing tight Hamilton cycles in 3-uniform hypergraphs
Random Structures & Algorithms
Random Structures & Algorithms
Approximate Hamilton decompositions of random graphs
Random Structures & Algorithms
Signless Laplacian eigenvalues and circumference of graphs
Discrete Applied Mathematics
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In this article we study Hamilton cycles in sparse pseudo-random graphs. We prove that if the second largest absolute value λ of an eigenvalue of a d-regular graph G on n vertices satisfies $$\lambda \leq{{(\log \, \log \, n)^2}\over {1000\, \log \, n \, (\log \, \log \, \log \, n)}}d$$ and n is large enough, then G is Hamiltonian. We also show how our main result can be used to prove that for every c 0 and large enough n a Cayley graph X (G,S), formed by choosing a set S of c log5 n random generators in a group G of order n, is almost surely Hamiltonian. © 2002 Wiley Periodicals, Inc. J Graph Theory 42: 17–33, 2003