Bounding the maximum size of a packet radio network

The author addresses the problem, arising in the topology design of packet radio networks (PRNs) which use time-division multiplexing and have a diameter constraint, of what is the maximum number n_c(f,k) of users which can be contained in a diameter-k PRN with f time slots per frame. The author assumed that users cannot transmit and receive simultaneously and cannot transmit/receive more than one packet at a time. This assumption implies that no two channels accessed by the same user may be assigned the same time slot. It is shown that the problem of determining n_c(f,k) is identical to the problem of determining the largest number of vertices which can be contained in an f-edge colorable directed graph with diameter k. Lower bounds on n_c(f, k) for f/2, k=3, 4, 5, . . . are obtained by generating large graphs of this type. The graphs are constructed and colored by simple and fast procedures which are similar for different values of f and k. An extensive bibliography on the edge-coloring problem is included