Resumen de A sufficient condition for the existence of a k-factor excluding a given r-factor

Sizhong Zhou, Lan Xu, Yang Xu

• Let G be a graph, and let k,r be nonnegative integers with k≥2. A k-factor of G is a spanning subgraph F of G such that dF(x)=k for each x∈V(G), where dF(x) denotes the degree of x in F. For S⊆V(G), NG(S)=⋃x∈SNG(x). The binding number of G is defined by bind(G)=min{|NG(S)||S|:∅≠S⊂V(G),NG(S)≠V(G)}. In this paper, we obtain a binding number and neighborhood condition for a graph to have a k-factor excluding a given r-factor. This result is an extension of the previous results.