Publication Date

May 2022


An even 2-factor is one such that each cycle is of even length. A 4- regular graph G is 4-edge-colorable if and only if G has two edge-disjoint even 2- factors whose union contains all edges in G. It is known that the line graph of a cubic graph without 3-edge-coloring is not 4-edge-colorable. Hence, we are interested in whether those graphs have an even 2-factor. Bonisoli and Bonvicini proved that the line graph of a connected cubic graph G with an even number of edges has an even 2-factor, if G has a perfect matching [Even cycles and even 2-factors in the line graph of a simple graph, Electron. J. Combin. 24 (2017), P4.15]. In this paper, we extend this theorem to the line graph of a connected cubic graph G satisfying certain conditions.

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This work is licensed under a Creative Commons Attribution 4.0 License.