Vertex-Disjoint Triangles in Claw-Free Graphs with Minimum Degree at Least Three

. Our main result is as follows: For any integer , if G is a claw-free graph of order at least and with minimum degree at least 3, then G contains k vertex-disjoint triangles unless G is of order and G belongs to a known class of graphs. We also construct a claw-free graph with minimum degree 3 on n vertices for each such that it does not contain k vertex-disjoint triangles. We put forward a conjecture on vertex-disjoint triangles in -free graphs. Received: November 21, 1996/Revised: Revised February 19, 1998