Two operations on a graph preserving the (non)existence of 2-factors in its line graph

Abstract

Abstract. Let G = (V (G), E(G)) be a graph. Gould and Hynds (1999) showed a wellknown characterization of G by its line graph L(G) that has a 2-factor. In this paper, by defining two operations, we present a characterization for a graph G to have a 2-factor in its line graph2}] is connected. By applying the new characterization, we prove that every claw-free graph in which every edge lies on a cycle of length at most five and in which every vertex of degree two that lies on a triangle has two N 2 -locally connected adjacent neighbors, has a 2-factor. This result generalizes the previous results in papers : Li, Liu (1995) and Tian, Xiong, Niu (2012), and is the best possible.