POWRE: Distance Graphs and Channel Assignment Problems

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This project initiates further research on the fields of distancegraphs and the channel assignment (also named T-coloring). Bothfields have been active research areas for years.There are two major components in this project. The first oneextends research on problems on distance graphs and T-coloringand their connections. The first connection between distancegraphs and T-coloring was proved by the PI [1997] and was used toobtain extend solutions on a problem on distance graphs raisedand studied by Eggleton, Erdos and Skilton [1985]. A joint workwith Chang and Zhu [1997] completely solved the problem andproved the second connection which showed that the fractionalchromatic number of a distance graph is equal to its asymptoticT-coloring ratio. The latter parameter was shown, by Griggs andthe PI [1996], to be closely related to an earlier number theoryproblem, namely, density of sequences with missing differences,studied by Cantor and Gordon [1975] and by Haralambis [1977]. Theproject will follow this direction of research to explore otheruseful connections between distance graphs and T-coloring, toobtain further results on distance graphs including theirchromatic number, circular chromatic number and fractionalchromatic number, and to study a generalization of the problem ofEggleton, Erdos and Skilton.Motivated from practical situations in the channel assignmentproblem, several variations of T-coloring have been studied. Thesecond part of this project will extend the research of the PI'spast and current work and joint work on two variations ofT-coloring, namely, no-hole T-coloring and distance two labelingsof graphs. Research on the distance two labelings will alsobenefit the practical two-level-interference channel assignmentproblem.For update references and works of this project, readers arewelcome 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).