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arXiv · 2305.02570

Extremal Results on Conflict-free Coloring

Sriram Bhyravarapu·Shiwali Gupta·Subrahmanyam Kalyanasundaram·Rogers Mathew
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Abstract

A conflict-free open neighborhood coloring of a graph is an assignment of colors to the vertices such that for every vertex there is a color that appears exactly once in its open neighborhood. For a graph $G$, the smallest number of colors required for such a coloring is called the conflict-free open neighborhood (CFON) chromatic number and is denoted by $\chi_{ON}(G)$. By considering closed neighborhood instead of open neighborhood, we obtain the analogous notions of conflict-free closed neighborhood (CFCN) coloring, and CFCN chromatic number (denoted by $\chi_{CN}(G)$). The notion of conflict-free coloring was introduced in 2002, and has since received considerable attention. In this paper, we study some extremal questions related to CFON and CFCN coloring.

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Sriram Bhyravarapu, Shiwali Gupta, Subrahmanyam Kalyanasundaram, Rogers Mathew. 2023-05-04. Extremal Results on Conflict-free Coloring. https://arxiv.org/abs/2305.02570

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