Disjoint \(K_{1,4}\) in Claw-Free Graphs with Minimum Degree at Least Four

A graph is said to be claw-free if it does not contain an induced subgraph isomorphic to \(K_{1,3}\). Let \(k\) be an integer with \(k \geq 2\). We prove that if \(G\) is a claw-free graph of order at least \(14k – 13\) and with minimum degree at least four, then \(G\) contains \(k\) vertex-disjoint copies of \(K_{1,4}\). This partially supports a conjecture proposed by Jiang, Chiba, Fujita and Yan.