English

Graph unique-maximum and conflict-free colorings

Discrete Mathematics 2009-12-17 v1 Computational Complexity

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.

Keywords

Cite

@article{arxiv.0912.3004,
  title  = {Graph unique-maximum and conflict-free colorings},
  author = {Panagiotis Cheilaris and Geza Toth},
  journal= {arXiv preprint arXiv:0912.3004},
  year   = {2009}
}
R2 v1 2026-06-21T14:24:18.547Z