A strong edge coloring is an edge coloring of a simple graph in which every color class is an induced matching. Thus edges of the same color neither share a graph vertex nor have endpoints joined by another graph edge (Faudree et al. 1990).
The strong chromatic index is the least number of colors in such a coloring. It equals the chromatic number of the graph
square of the line graph. The Erdős-Nešetril
conjecture predicts an upper bound of 
, where 
is the maximum vertex degree.
