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The Parity of Directed Hamiltonian Cycles

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

preprint2013arXivOpen access
Andreas BjörklundThore Husfeldt
Data Structures and Algorithms
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Andreas BjörklundThore Husfeldt

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