Path factors and line graphs

Ando et al. [K. Ando, Y. Egawa, A. Kaneko, K. Kawarabayashi, H. Matsuda, Path factors in claw-free graphs, Discr. Math. 243 (2002) 195–200] proved that in a connected claw-free graph with minimum degree at least d there is a path factor having each path of length at least d. They conjectured that in a 2-connected case there is a path factor in which each path is of length at least 3 d + 2 . e a proof of this conjecture for the class of 2-connected line graphs.