Table of Contents
International Journal of Combinatorics
Volume 2015, Article ID 513073, 6 pages
http://dx.doi.org/10.1155/2015/513073
Research Article

Hamilton Paths and Cycles in Varietal Hypercube Networks with Mixed Faults

Department of Mathematics, University of Science and Technology of China, Wentsun Wu Key Laboratory of CAS, Hefei, Anhui 230026, China

Received 16 September 2014; Accepted 5 January 2015

Academic Editor: Chris A. Rodger

Copyright © 2015 Jian-Guang Zhou and Jun-Ming Xu. 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

This paper considers the varietal hypercube network with mixed faults and shows that contains a fault-free Hamilton cycle provided faults do not exceed for and contains a fault-free Hamilton path between any pair of vertices provided faults do not exceed for . The proof is based on an inductive construction.