Hamiltonian Paths in Cartesian Powers of Directed Cycles
Combinatorics
2007-05-23 v1
Abstract
The vertex set of the kth cartesian power of a directed cycle of length m can be naturally identified with the set of k-tuples of integers modulo m. For any two vertices v and w of this graph, it is easy to see that if there is a hamiltonian path from v to w, then the sum of the coordinates of v is congruent, modulo m, to one more than the sum of the coordinates of w. We prove the converse, unless k = 2 and m is odd.
Keywords
Cite
@article{arxiv.math/0110073,
title = {Hamiltonian Paths in Cartesian Powers of Directed Cycles},
author = {David Austin and Heather Gavlas and Dave Witte},
journal= {arXiv preprint arXiv:math/0110073},
year = {2007}
}
Comments
8 pages, no figures