The Path Partition Conjecture is true for claw-free graphs Original Research Article

The detour order of a graph image, denoted by image, is the order of a longest path in image. The Path Partition Conjecture (PPC) is the following: If image is any graph and image any pair of positive integers such that image, then the vertex set of image has a partition image such that image and image. We prove that this conjecture is true for the class of claw-free graphs. We also show that to prove that the PPC is true, it is sufficient to consider the class of 2-connected graphs.