Relations with the modeling of channel assignment problems on multi-hop wireless networks and edge coloring problems of graphs

Multi-hop wireless networks [1] are autonomous systems of mobile nodes connected by wireless links and consist of nodes and wireless links. The nodes are classified into two kinds: one is a mobile terminal such as mobile phone, personal computer, handheld computer, Personal Digital Assistant (PDA) and so on, each of which has a router communication function for other terminals and the other is a special terminal that acts only as a router for mobile terminals and has a long-life or a permanent battery(Fig.1). Such multi-hop wireless networks are useful in various applications when cellular infrastructure is neither available nor realistic or when ubiquitous communication services are required without the presence or use of a fixed infrastructure. For multi-hop wireless networks, we assign channels to communication between two terminals. This channel assignment problems are modelled to edge coloring problems in graph theory. In the previous paper[4],[6] we defined a new edge coloring problem called middle edge coloring and discussed the property of the coloring. In this paper, we consider appropriate models of the channel assignment problems.