Stability Number and \(f\)-factor in \(K_{1,n}\)-free Graphs

Abstract

Let \(G\) be a graph with vertex set \(V(G)\) and let \(f\) be a nonnegative integer-valued function defined on \(V(G)\). A spanning subgraph \(F\) of \(G\) is called an \(f\)-factor if \(d_F(x) = f(x)\) for every \(x \in V(F)\). In this paper, we present some sufficient conditions for the existence of \(f\)-factors and connected \((f-2, f)\)-factors in \(K_{1,n}\)-free graphs. The conditions involve the minimum degree, the stability number, and the connectivity of graph \(G\).