Abstract
The star chromatic index chi'_s(G) of a graph G is the minimum number of colors needed to properly color the edges of the graph so that no path or cycle of length four is bi-colored. We obtain a near-linear upper bound in terms of the maximum degree Delta=Delta(G).
Our best lower bound on chi'_s in terms of Delta is 2Delta(1+o(1)) valid for complete graphs. We also consider the special case of cubic graphs, for which we show that the star chromatic index lies between 4 and 7 and characterize the graphs attaining the lower bound.
The proofs involve a variety of notions from other branches of mathematics and may therefore be of certain independent interest.