English

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.

Keywords

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}
}
R2 v1 2026-06-21T22:01:56.531Z