English

The Parity of Directed Hamiltonian Cycles

Data Structures and Algorithms 2013-08-09 v2

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(1.619^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.

Keywords

Cite

@article{arxiv.1301.7250,
  title  = {The Parity of Directed Hamiltonian Cycles},
  author = {Andreas Björklund and Thore Husfeldt},
  journal= {arXiv preprint arXiv:1301.7250},
  year   = {2013}
}