Counting edge-Kempe-equivalence classes for 3-edge-colored cubic graphs

Two n -edge colorings of a graph are edge-Kempe equivalent if one can be obtained from the other by a series of edge-Kempe switches. In this work we show every planar bipartite cubic graph has exactly one edge-Kempe equivalence class, when 3 = χ ′ ( G ) colors are used. In contrast, we also exhibit infinite families of nonplanar bipartite cubic (and thus 3-edge colorable) graphs with a range of numbers of edge-Kempe equivalence classes when using 3 colors. These results address a question raised by Mohar.