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On Cui-Kano's Characterization Problem on Graph Factors



An math formula-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 math formula in F, where math formula. In this article, we investigate math formula-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 math formula-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.