On the number of Hamilton cycles in pseudo-random graphs

Details On the number of Hamilton cycles in pseudo-random graphs On the number of Hamilton cycles in pseudo-random graphs

2011-11-27

arxiv.org/abs/1111.6261v2

Mathematics

Combinatorics

Scientific paper

We prove that if G is an (n,d,lambda)-graph (a d-regular graph on n vertices, all of whose non-trivial eigenvalues are at most lambda) and the following conditions are satisfied: 1. d/lambda >= (log n)^{1+epsilon} for some constant epsilon>0; 2.log d * lod (d/lambda) >> log n, then the number of Hamilton cycles in G is n!(d/n)^n(1+o(1))^n.

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