An Even 2-Factor in the Line Graph of a Cubic Graph

Authors

SeungJae Eom, Yokohama National UniversityFollow
Kenta Ozeki, Yokohama National UniversityFollow

Publication Date

May 2022

Abstract

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.

Creative Commons License

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

Recommended Citation

Eom, SeungJae and Ozeki, Kenta (2022) "An Even 2-Factor in the Line Graph of a Cubic Graph," Theory and Applications of Graphs: Vol. 9: Iss. 1, Article 7.
DOI: 10.20429/tag.2022.090107
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol9/iss1/7