Table of Contents
Journal of Discrete Mathematics
Volume 2016, Article ID 7942192, 5 pages
http://dx.doi.org/10.1155/2016/7942192
Research Article

Dicycle Cover of Hamiltonian Oriented Graphs

1Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia
2Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA
3College of Mathematics Sciences, Xinjiang Normal University, Urumqi 830054, China

Received 9 October 2015; Accepted 31 December 2015

Academic Editor: Kinkar Ch Das

Copyright © 2016 Khalid A. Alsatami et al. 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

A dicycle cover of a digraph is a family of dicycles of such that each arc of lies in at least one dicycle in . We investigate the problem of determining the upper bounds for the minimum number of dicycles which cover all arcs in a strong digraph. Best possible upper bounds of dicycle covers are obtained in a number of classes of digraphs including strong tournaments, Hamiltonian oriented graphs, Hamiltonian oriented complete bipartite graphs, and families of possibly non-Hamiltonian digraphs obtained from these digraphs via a sequence of 2-sum operations.