Path-related vertex colorings of graphs

We investigate algorithms for a frequency assignment problem in cellular networks. The problem can be modeled as a special coloring problem for graphs. Base stations are the vertices, ranges are the paths in the graph, and colors (frequencies) must be assigned to vertices following the conflict-free property: In every path there is a color that occurs exactly once. We concentrate on the special case where the base stations lie on a chain and ranges are the non-empty subchains. We also consider other simple graphs, such as rings, trees, and grids. We discuss a whole hierarchy of related coloring problems. This work was supported by the European Social Fund (75%) and National Resources (25%) under the program EPEAEK II, `Heraclitus'.