Disjoint K 4 − in claw-free graphs with minimum degree at least five

Abstract

A graph is said to be claw-free if it does not contain an induced subgraph isomorphic to K1,3. Let K4− be the graph obtained by removing exactly one edge from K4 and let k be an integer with k ⩾ 2. We prove that if G is a claw-free graph of order at least 13k − 12 and with minimum degree at least five, then G contains k vertex-disjoint copies of K4−. The requirement of number five is necessary.