Counting edge-Kempe-equivalence classes for 3-edge-colored cubic graphs
Combinatorics
2012-09-11 v1
Abstract
Two edge colorings of a graph are {\em edge-Kempe equivalent} if one can be obtained from the other by a series of edge-Kempe switches. This work gives some results for the number of edge-Kempe equivalence classes for cubic graphs. In particular we show every 2-connected planar bipartite cubic graph has exactly one edge-Kempe equivalence class. Additionally, we exhibit infinite families of nonplanar bipartite cubic graphs with a range of numbers of edge-Kempe equivalence classes. Techniques are developed that will be useful for analyzing other classes of graphs as well.
Cite
@article{arxiv.1209.1730,
title = {Counting edge-Kempe-equivalence classes for 3-edge-colored cubic graphs},
author = {sarah-marie belcastro and Ruth Haas},
journal= {arXiv preprint arXiv:1209.1730},
year = {2012}
}