\([a, b]\)-Factors With Given Edges In Graphs

Abstract

Let \(G\) be a graph, and let \(a\) and \(b\) be integers with \(1 \leq a \leq b\). An \([a, b]\)-factor of \(G\) is defined as a spanning subgraph \(F\) of \(G\) such that \(a \leq d_F(v) \leq b\) 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.