Unique-Maximum and Conflict-Free Coloring for Hypergraphs and Tree Graphs
We investigate the relationship between two kinds of vertex colorings of hypergraphs: unique-maximum colorings and conflict-free colorings. In a unique-maximum coloring, the colors are ordered, and in every hyperedge of the hypergraph the maximum color in the hyperedge occurs in only one vertex of the hyperedge. In a conflict-free coloring, in every hyperedge of the hypergraph there exists a color in the hyperedge that occurs in only one vertex of the hyperedge. We define corresponding unique-maximum and conflict-free chromatic numbers and investigate their relationship in arbitrary hypergraphs. Then, we concentrate on hypergraphs that are induced by simple paths in tree graphs.
KeywordsChromatic Number Parity Vector Tree Graph Central Edge Vertex Coloring
Unable to display preview. Download preview PDF.
- 4.Cheilaris, P.: Conflict-free coloring. Ph.D. thesis, City University of New York (2009)Google Scholar
- 12.Leiserson, C.E.: Area-efficient graph layouts (for VLSI). In: Proceedings of the 21st Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 270–281 (1980)Google Scholar
- 18.Pothen, A.: The complexity of optimal elimination trees. Tech. Rep. CS-88-16, Department of Computer Science, Pennsylvania State University (1988)Google Scholar
- 19.Smorodinsky, S.: Combinatorial Problems in Computational Geometry. Ph.D. thesis, School of Computer Science, Tel-Aviv University (2003)Google Scholar