A new coloring problem of networks related to a channel assignment problem in cellular mobile systems

Recently, a new channel assignment scheme has been proposed (K. Nakano, 1989). This scheme takes the degree of interference into consideration. In the scheme, a channel is simultaneously assigned if the carrier-to-interference ratio is more than the desired value. The authors formulate this new model using a network and a new coloring problem of networks. They show that the new coloring problem is a generalization of the usual coloring problem of graphs and describe some results concerned with this coloring problem. One of the merits of this formulation is that the degree of cochannel interference between cells can be represented