Abstract
In 2008, it is shown that if H≅K1,3 (the claw), then every H-free graph G has an even factor if and only if δ(G)≥2 and every odd branch-bond of G having an edge-branch. In this paper, we characterize all connected graphs H with order at least three such that every H-free graph has an even factor if and only if δ(G)≥2 and every odd branch-bond of G has an edge-branch.
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