An Exact Bound on the Number of Proper 3-Edge-Colorings of a Connected Cubic Graph

The paper examines the question of an upper bound on the number of proper edge 3-colorings of a connected cubic graph with 2 n vertices. For this purpose, the Karpov method is developed with the help of which a weaker version of the bound was previously obtained. Then the bound 2 n + 8 for even n and 2 n + 4 for odd n is proved. Moreover, a unique example is found, for which the upper bound is exact.