Graph coloring bounds for cellular radio

AbstractA graph coloring problem useful in deciding whether a set of call requests in cellular radio is compatible with frequency use constraints is introduced. Lower and upper bounds are obtained for the hexagonal cell case typical of many urban cellular systems. These bounds are on the number of frequencies needed to satisfy demand when there is an upper bound on the demand with small subsets. For example, if we have 308 frequency channels available, as for American cellular systems, then this is enough to satisfy any set of call requests when every “superhex” of 7 hexagons, 6 around 1, has at most 154 call requests. But 308 frequencies are definitely not enough if we permit some superhexes to have 206 or more call requests