# Search Results

## 1 - 1 of 1 items :

- Author: Yang Yang x

- Life Sciences, other x

- General Mathematics x

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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 *d _{F}*(

*x*) =

*k*for each

*x*∈

*V*(

*G*), where

*d*(

_{F}*x*) denotes the degree of

*x*in

*F*. For

*S*⊆

*V*(

*G*),

*N*(

_{G}*S*) = ∪

_{x∊S}

*N*(

_{G}*x*). The binding number of

*G*is defined by

*bind*

*k*-factor excluding a given

*r*-factor. This result is an extension of the previous results.