The Parity of Directed Hamiltonian Cycles

Published 30 Jan 2013 in cs.DS | (1301.7250v2)

Abstract: We present a deterministic algorithm that given any directed graph on n vertices computes the parity of its number of Hamiltonian cycles in O(1.619ⁿ⁾ time and polynomial space. For bipartite graphs, we give a 1.5ⁿ poly(n) expected time algorithm. Our algorithms are based on a new combinatorial formula for the number of Hamiltonian cycles modulo a positive integer.

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