$[a,b]$-Factors With Given Edges In Graphs

Abstract

Let $G$ be a graph, and let $a$ and $b$ be integers with $1\le a\le b$. An $[a,b]$-factor of $G$ is defined as a spanning subgraph $F$ of $G$ such that $a\le d_F(v)\le b$ for each $v\in V(G)$. In this paper, we obtain a sufficient condition for a graph to have $[a,b]$-factors including given edges, extending a well-known sufficient condition for the existence of a $k$-factor.