Strong edge colorings of graphs and the covers of Kneser graphs [Elektronski vir]
Lužar, Borut ...
A proper edge coloring of a graph is strong if it creates no bichromatic path of length three. It is well known that for a strong edge coloring of a ▫$k$▫-regular graph at least ▫$2k − 1$▫ colors are ...needed. We show that a ▫$k$▫-regular graph admits a strong edge coloring with ▫$2k − 1$▫ colors if and only if it covers the Kneser graph ▫$K(2k − 1, k − 1)$▫. In particular, a cubic graph is strongly 5-edge-colorable whenever it covers the Petersen graph. One of the implications of this result is that a conjecture about strong edge colorings of subcubic graphs proposed by Faudree et al. is false.
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