The existence of even factors in iterated line graphs

An even factor of a graph is a spanning subgraph of G in which all degrees are even, positive integers. In this paper, we characterize the claw-free graphs having even factors and then prove that the n-iterated line graph Lⁿ(G) of G has an even factor if and only if every end branch of G has length at most n and every odd branch-bond of G has a branch of length at most n+1.