A Kempe switch of a 3-edge-coloring of a cubic graph G on a bicolored cycle C swaps the colors on C and gives rise to a new 3-edge-coloring of G. Two 3-edge-colorings of G are Kempe equivalent if they can be obtained from each other by a sequence of Kempe switches. Fisk proved that any two 3-edge-colorings in a cubic bipartite planar graph are Kempe equivalent. In this paper, we obtain an analog of this theorem and prove that all 3-edge-colorings of a cubic bipartite projective-planar graph G are pairwise Kempe equivalent if and only if G has an embedding in the projective plane such that the chromatic number of the dual triangulation G* is at least 5. As a by-product of the results in this paper, we prove that the list-edge-coloring conjecture holds for cubic graphs G embedded on the projective plane provided that the dual G* is not 4-vertex-colorable.

双色循环C上三次图G的 3 边着色的 Kempe 开关交换C上的颜色并产生G的新 3 边着色。如果G的两个 3 边着色可以通过一系列 Kempe 开关相互获得，则它们是 Kempe 等价的。Fisk 证明了三次二部平面图中的任何两个 3 边着色都是 Kempe 等价的。在本文中，我们获得了该定理的类比，并证明了当且仅当G在投影平面中嵌入使得色数对偶三角剖分G* 至少为 5。作为本文结果的副产品，我们证明了列表边着色猜想适用于嵌入在投影平面上的三次图G，前提是对偶G * 不是 4-顶点-可着色。