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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 5384190, 7 pages
Research Article

Complementary Cycles in Irregular Multipartite Tournaments

1School of Mathematics and Information Science, Yantai University, Yantai 264005, China
2Chifeng University, Chifeng 024000, China
3College of Computer Science and Technology, Shandong University, Jinan 250101, China

Received 29 March 2016; Accepted 17 July 2016

Academic Editor: Sergii V. Kavun

Copyright © 2016 Zhihong He 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.


A tournament is a directed graph obtained by assigning a direction for each edge in an undirected complete graph. A digraph is cycle complementary if there exist two vertex disjoint cycles and such that . Let be a locally almost regular -partite tournament with and such that all partite sets have the same cardinality , and let be a -cycle of . In this paper, we prove that if has no cycle factor, then contains a pair of disjoint cycles of length and , unless is isomorphic to , , , or .