2-factors in claw-free graphs with locally disconnected vertices
An edge of is singular if it does not lie on any triangle of ; otherwise, it is non-singular. A vertex of a graph is called locally connected if the induced subgraph by its neighborhood is connected; otherwise, it is called locally disconnected. In this paper, we prove that if a connected claw-free graph of order at least three satisfies the following two conditions: (i) for each locally disconnected vertex of degree at least in there is a nonnegative integer such that lies...