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arXiv · 2105.01363

Switching 3-edge-colorings of cubic graphs

Jan Goedgebeur·Patric R. J. Östergård
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Abstract

The chromatic index of a cubic graph is either 3 or 4. Edge-Kempe switching, which can be used to transform edge-colorings, is here considered for 3-edge-colorings of cubic graphs. Computational results for edge-Kempe switching of cubic graphs up to order 30 and bipartite cubic graphs up to order 36 are tabulated. Families of cubic graphs of orders $4n+2$ and $4n+4$ with $2^n$ edge-Kempe equivalence classes are presented; it is conjectured that there are no cubic graphs with more edge-Kempe equivalence classes. New families of nonplanar bipartite cubic graphs with exactly one edge-Kempe equivalence class are also obtained. Edge-Kempe switching is further connected to cycle switching of Steiner triple systems, for which an improvement of the established classification algorithm is presented.

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Jan Goedgebeur, Patric R. J. Östergård. 2021-05-04. Switching 3-edge-colorings of cubic graphs. https://arxiv.org/abs/2105.01363

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