A short note on conflict-free coloring on closed neighborhoods of bounded degree graphs

Bhyravarapu, S. and Kalyanasundaram, S. and Mathew, R. (2021) A short note on conflict-free coloring on closed neighborhoods of bounded degree graphs. Journal of Graph Theory, 97 (4). pp. 553-556. ISSN 03649024

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Abstract

he closed neighborhood conflict-free chromatic number of a graph (Formula presented.), denoted by (Formula presented.), is the minimum number of colors required to color the vertices of (Formula presented.) such that for every vertex, there is a color that appears exactly once in its closed neighborhood. Pach and Tardos showed that (Formula presented.), for any (Formula presented.), where (Formula presented.) is the maximum degree. In 2014, Glebov et al. showed existence of graphs (Formula presented.) with (Formula presented.). In this article, we bridge the gap between the two bounds by showing that (Formula presented.).

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