Relations on the bounds of the number of channels on multi-hop wireless networks

For multi-hop wireless networks, we assign channels to communication between terminals. For this assignment problem, modeling using the edge coloring of the graph theory has been proposed. In the modeling, all edges of the graph are assigned colors. In this paper, we assign colors to edges in a subset of the edge set as the other modeling, and we consider the number of assigned colors in the graph. We show some theoretical results and examine this modeling with computer simulation.