Abstract
We investigate the relationship between two kinds of vertex colorings of graphs: unique-maximum colorings and conflict-free colorings. In a unique-maximum coloring, the colors are ordered, and in every path of the graph the maximum color appears only once. In a conflict-free coloring, in every path of the graph there is a color that appears only once. We also study computational complexity aspects of conflict-free colorings and prove a completeness result. Finally, we improve lower bounds for those chromatic numbers of the grid graph. © 2010 Springer-Verlag Berlin Heidelberg.
Cite
CITATION STYLE
Cheilaris, P., & Tóth, G. (2010). Graph unique-maximum and conflict-free colorings. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6078 LNCS, pp. 143–154). https://doi.org/10.1007/978-3-642-13073-1_14
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