Vertex disjoint copies of K1,4 in claw-free graphs

Abstract A complete bipartite graph with partite sets X and Y , where | X | = 1 and | Y | = r , is denoted by K 1 , r . A graph G is said to be claw-free if G does not contain K 1 , 3 as an induced subgraph. There are several well-known and important families of graphs that are claw-free such as line graphs and complements of triangle-free graphs. Claw-free graphs have numerous interesting properties and applications. This paper considers vertex disjoint K 1 , 4 s in claw-free graphs. Let k be an integer with k ≥ 2 and let G be a claw-free graph with | V ( G ) | ≥ 10 k − 9 . We prove that if the minimum degree of G is at least 4, then it contains k vertex disjoint K 1 , 4 s. This result answers the question in [Jiang, Chiba, Fujita, Yan, Discrete Math. 340 (2017) 649–654].