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Keywords:

  • Lovász's structural description;
  • inline image-factor;
  • inline image-decomposition
  • 2010 AMS Classification;
  • 05C75

Abstract

An inline image-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 inline image in F, where inline image. In this article, we investigate inline image-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 inline image-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.