Graph unique-maximum and conflict-free colorings

We investigate the relationship between two kinds of vertex colorings of graphs: uniquemaximum 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.

• Type: Conference
• Year: 2010
• Where: CIAC
• Authors: Panagiotis Cheilaris and Géza Tóth
• Keywords: Algorithms, CIAC 2010, Conflict-free Colorings, Uniquemaximum Colorings, Vertex Colorings