Complex sentence: Many variations of the edge coloring problem, asking for assignments of colors to edges that satisfy other conditions than non-adjacency, have been studied, and edge colorings have applications in scheduling problems and in frequency assignment in fiber optic networks.
Split into simpler sentences: Many variations of the edge coloring problem, in which an assignments of colors to edges must satisfy other conditions than non-adjacency, have been studied. Edge colorings have applications in scheduling problems and in frequency assignment for fiber optic networks.