Induced claws and existence of even factors of graphs

An even factor of a graph G is a spanning subgraph in G such that the degree of each vertex is a positive even integer. In this paper, we show that for any induced claw of simple graph G of order at least 10, if there exists at least a pair of vertices out of the claw such that they are the common neighbors of nonadjacent vertices of the claw, then G has an even factor if and only if \(\delta (G)\ge 2\) and every odd branch-bond of G contains a branch of length 1. The even factor of claw-heavy graphs was also characterized.