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The Parity of Directed Hamiltonian Cycles
2013
2013 IEEE 54th Annual Symposium on Foundations of Computer Science
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We present a deterministic algorithm that given any directed graph on n vertices computes the parity of its number of Hamiltonian cycles in O(1.618 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.
doi:10.1109/focs.2013.83
dblp:conf/focs/BjorklundH13
fatcat:w743xxvwvfgotiq4hogn47gc5a