This project initiates further research on the fields of distance graphs and the channel assignment (also named T-coloring). Both fields have been active research areas for years.
There are two major components in this project. The first one extends research on problems on distance graphs and T-coloring and their connections. The first connection between distance graphs and T-coloring was proved by the PI [1997] and was used to obtain extend solutions on a problem on distance graphs raised and studied by Eggleton, Erdos and Skilton [1985]. A joint work with Chang and Zhu [1997] completely solved the problem and proved the second connection which showed that the fractional chromatic number of a distance graph is equal to its asymptotic T-coloring ratio. The latter parameter was shown, by Griggs and the PI [1996], to be closely related to an earlier number theory problem, namely, density of sequences with missing differences, studied by Cantor and Gordon [1975] and by Haralambis [1977]. The project will follow this direction of research to explore other useful connections between distance graphs and T-coloring, to obtain further results on distance graphs including their chromatic number, circular chromatic number and fractional chromatic number, and to study a generalization of the problem of Eggleton, Erdos and Skilton.
Motivated from practical situations in the channel assignment problem, several variations of T-coloring have been studied. The second part of this project will extend the research of the PI's past and current work and joint work on two variations of T-coloring, namely, no-hole T-coloring and distance two labelings of graphs. Research on the distance two labelings will also benefit the practical two-level-interference channel assignment problem.
For update references and works of this project, readers are welcome to visit the PI's web site at: www.calstatela.edu/faculty/dliu/dliu.htm or email to: dliu@calstatela.edu.
This POWRE project is supported by the MPS Office of Multidisciplinary Activities (OMA).
