Parameterized algorithms for conflict-free colorings of graphs

We also study the complexity of the problem on special graph classes. For split graphs, we give a polynomial time algorithm for closed neighborhood conflict-free coloring problem, whereas we show that open neighborhood conflict-free coloring is NP-complete. For cographs, we show that conflict-free closed neighborhood coloring can be solved in polynomial time and conflict-free open neighborhood coloring need at most three colors. We show that interval graphs can be conflict-free colored using at most four colors.