Vertex-disjoint K 1 + (K 1 . K 2) in K 1,4-free graphs with minimum degree at least four

A graph is said to be K 1,4-free if it does not contain an induced subgraph isomorphic to K 1,4. Let k be an integer with k . 2. We prove that if G is a K 1,4-free graph of order at least 11k-10 with minimum degree at least four, then G contains k vertex-disjoint copies of K 1 + (K 1 . K 2).