Matching extension in \(K_{1,r}\)-free graphs with independent claw centers (Q1356714)

If every set of \(k\) independent edges of a graph \(G\) is extendible to a perfect matching, then the graph \(G\) is called \(k\)-extendible. The main result of this paper is the following theorem: Let \(G\) be an even \((2k+1)\)-connected \(K_{1,k+3}\)-free graph such that the set of all centers of claws is independent. Then \(G\) is \(k\)-extendible. The author goes on to obtain an analogous result on the \(k\)-extendibility of almost claw-free graphs and for claw-free graphs. An example showing that the assumption that the graph \(G\) is \(K_{1,k+3}\)-free is sharp.