T-colorings of multigraphs in frequency assignment

We deal with the problem of frequency assignment in mobile and general radio networks, where the signal interferences are modeled using an interference graph G. Our approach uses graph theoretic and optimization techniques. The frequency assignment problem can be cast as a variant of the vertex coloring problem(called the T-colorings problem) on graphs. In this paper, we will show several previous results of multigraphs, and we also will present a new algorithm to compute the T-coloring span of multigraphs.