On Cui-Kano's Characterization Problem on Graph Factors
Article first published online: 2 JAN 2013
© 2013 Wiley Periodicals, Inc.
Journal of Graph Theory
Volume 74, Issue 3, pages 335–343, November 2013
How to Cite
Lu, H. and Wang, D. G.L. (2013), On Cui-Kano's Characterization Problem on Graph Factors. J. Graph Theory, 74: 335–343. doi: 10.1002/jgt.21712
- Issue published online: 5 SEP 2013
- Article first published online: 2 JAN 2013
- Manuscript Revised: 25 AUG 2012
- Manuscript Received: 27 SEP 2011
- National Natural Science Foundation of China. Grant Numbers: 11101329, 11101010
- Fundamental Research Funds for the Central Universities
- Lovász's structural description;
- 2010 AMS Classification;
An -factor of a graph G is defined to be a spanning subgraph F of G such that each vertex has a degree belonging to the set in F, where . In this article, we investigate -factors of graphs by using Lovász's structural descriptions to the degree prescribed subgraph problem. We find some sufficient conditions for the existence of an -factor of a graph. In particular, we make progress on the characterization problem for a special family of graphs proposed by Cui and Kano in 1988.