International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 597408, 8 pages
Research Article

Bipartite Toughness and k-Factors in Bipartite Graphs

Guizhen Liu,1 Jianbo Qian,2 Jonathan Z. Sun,3 and Rui Xu4

1School of Mathematics and System Sciences, Shandong University, Jinan 250100, China
2Department of Computer Science, Memorial University of Newfoundland, St. John's, NL, A1B 3X5, Canada
3School of Computing, The University of Southern Mississippi, Hattiesburg, MS 39406, USA
4Department of Mathematics, College of Arts and Sciences, The State University of West Georgia, Carrollton, GA 30118, USA

Received 18 August 2008; Accepted 7 October 2008

Academic Editor: Siamak Yassemi

Copyright © 2008 Guizhen Liu 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.


We define a new invariant tB(G) in bipartite graphs that is analogous to the toughness t(G) and we give sufficient conditions in term of tB(G) for the existence of k-factors in bipartite graphs. We also show that these results are sharp.