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

Extremal Results on Conflict-free Coloring