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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 ak    $k$   ‐regular graph at least2  k  −  1    $2k-1$    colors are needed. We show that ak    $k$   ‐regular graph admits a strong edge coloring with2  k  −  1    $2k-1$    colors if and only if it covers the Kneser graphK   (   2  k  −  1  ,  k  −  1   )$K(2k-1,k-1)$   . 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.

Strong edge colorings of graphs and the covers of Kneser graphs