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

Abstract

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 xV (G), where dF(x) denotes the degree of x in F. For SV (G), NG(S) = ∪xS NG(x). The binding number of G is defined by bind (G)=min{|NG(S)||S|:SV(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.

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