Vertex-disjoint copies of [formula omitted] in claw-free graphs

Abstract

A graph G is said to be claw-free if G does not contain an induced subgraph isomorphic to K 1 , 3 . Let k be an integer with k ⩾ 2 . We prove that if G is a claw-free graph of order at least 7 k - 6 and with minimum degree at least 3, then G contains k vertex-disjoint copies of K 1 + ( K 1 ∪ K 2 ) .