Erratum to: Conflict-Free Chromatic Art Gallery Coverage

Abstract

The authors wish to acknowledge a mistake in the Related Work Section of the paper “Conflict-Free Chromatic Art Gallery Coverage” [1], where we mentioned conflictfree colorings of hypergraphs. In the conflict-free coloring of a hypergraph H , every edge e (a subset of vertices) must have a vertex that is uniquely colored among the vertices in e. For instance, consider the geometric hypergraph induced by axis-aligned rectangles: Its vertices correspond to a finite set of axis-aligned rectangles, and each maximal subset of rectangles with a common intersection forms a hyperedge. We erroneously wrote that for these hypergraphs, the conflict-free chromatic number has a tight Θ(logn) bound, but in fact only an upper bound of O(log2 n) (shown by Smorodinsky in [3]), and a lower bound of Ω(logn) (given by Pach and Tardos in [2]) is known.