On Cui-Kano's Characterization Problem on Graph Factors
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 Lovsz'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.
-factor lovsz's structural description -decomposition