On Cayley digraphs that do not have hamiltonian paths
Combinatorics
2013-06-25 v1
Abstract
We construct an infinite family of connected, 2-generated Cayley digraphs Cay(G;a,b) that do not have hamiltonian paths, such that the orders of the generators a and b are arbitrarily large. We also prove that if G is any finite group with |[G,G]| < 4, then every connected Cayley digraph on G has a hamiltonian path (but the conclusion does not always hold when |[G,G]| = 4 or 5).
Cite
@article{arxiv.1306.5443,
title = {On Cayley digraphs that do not have hamiltonian paths},
author = {Dave Witte Morris},
journal= {arXiv preprint arXiv:1306.5443},
year = {2013}
}
Comments
10 pages, plus 14-page appendix of notes to aid the referee