1 research outputs found
Strong edge colorings of graphs and the covers of Kneser graphs
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
-regular graph at least colors are needed. We show that a -regular
graph admits a strong edge coloring with colors if and only if it covers
the Kneser graph . In particular, a cubic graph is strongly
-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. [Ars Combin. 29 B (1990), 205--211]
is false