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.
Edge-coloring, Kempe chains, Coloring graphs, Cubic graphs
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Belcastro, Sarah-Marie and Haas, Ruth, "Counting Edge-Kempe-Equivalence Classes for 3-Edge-Colored Cubic Graphs" (2014). Faculty Publications. Paper 1.