The paper examines the question of an upper bound on the number of proper edge 3-colorings of a connected cubic graph with 2n 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 2n + 8 for even n and 2n + 4 for odd n is proved. Moreover, a unique example is found, for which the upper bound is exact.
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D. V. Karpov, “On proper 3-colorings of edges of a cubic graph,” Zap Nauchn. Semin. POMI, 488, 31–48 (2019).
N. J. A. Sloane (editor), The On-Line Encyclopedia of Integer Sequences, https://oeis.org.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 497, 2020, pp. 26–52.
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Ivanov, M.P. An Exact Bound on the Number of Proper 3-Edge-Colorings of a Connected Cubic Graph. J Math Sci 275, 130–146 (2023). https://doi.org/10.1007/s10958-023-06667-9
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DOI: https://doi.org/10.1007/s10958-023-06667-9