International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 597408, 8 pages
doi:10.1155/2008/597408
Bipartite Toughness and k-Factors in Bipartite Graphs
Guizhen Liu1
, Jianbo Qian2
, Jonathan Z. Sun3
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
Abstract
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.