Table of Contents
International Journal of Combinatorics
Volume 2013 (2013), Article ID 725809, 7 pages
http://dx.doi.org/10.1155/2013/725809
Research Article

On Cayley Digraphs That Do Not Have Hamiltonian Paths

Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, AB, Canada T1K 3M4

Received 23 June 2013; Accepted 4 November 2013

Academic Editor: Jun-Ming Xu

Copyright © 2013 Dave Witte Morris. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We construct an infinite family of connected, -generated Cayley digraphs that do not have hamiltonian paths, such that the orders of the generators and are unbounded. We also prove that if is any finite group with , then every connected Cayley digraph on has a hamiltonian path (but the conclusion does not always hold when or ).