Graph/network theory results are applicable to
problems in communications. As a representative example,
the node coloring problem in graph theory
is applicable to the channel assignment problem in
cellular mobile communication systems. The node
coloring problem is NP-complete, meaning that optimally
solving it is very difficult. Therefore, we use
heuristic algorithms for the channel assignment problem.
In this case, the graph theory results show the
legitimacy of using heuristic techniques. On the other
hand, we can directly apply graph theory to communication
problems. For example, on contents delivery
services in the Internet, we place mirror servers that
provide the same contents on the network. Location
problems on flow networks are applicable to mirror
server allocation problems. In a simple case, we can
efficiently solve the problem. In this paper, we concentrate
on multi-hop wireless networks and consider
the relationship between their problems and the results
of graph/network theory.