Counting Edge-Kempe-Equivalence Classes for 3-Edge-Colored Cubic Graphs

Authors

Sarah-Marie Belcastro, University of Massachusetts AmherstFollow
Ruth Haas, Smith CollegeFollow

Document Type

Article

Publication Date

6-28-2014

Publication Title

Discrete Mathematics

Abstract

Two edge colorings of a graph are 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

Edge-coloring, Kempe chains, Coloring graphs, Cubic graphs

Volume

325

First Page

77

Last Page

84

DOI

doi:10.1016/j.disc.2014.02.014

ISSN

0012-365X

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Comments

Peer reviewed accepted manuscript.

Recommended Citation

Belcastro, Sarah-Marie and Haas, Ruth, "Counting Edge-Kempe-Equivalence Classes for 3-Edge-Colored Cubic Graphs" (2014). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/1