Conflict-free coloring of graphs
نویسندگان
چکیده
We study the conflict-free chromatic number χCF of graphs from extremal and probabilistic point of view. We resolve a question of Pach and Tardos about the maximum conflict-free chromatic number an n-vertex graph can have. Our construction is randomized. In relation to this we study the evolution of the conflict-free chromatic number of the ErdősRényi random graph G(n, p) and give the asymptotics for p = ω(1/n). We also show that for p ≥ 1/2 the conflict-free chromatic number differs from the domination number by at most 3. MSC classes: 05C35, 05C15, 05C80, 05D40, 05C69.
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