Conflict-free coloring is a kind of vertex coloring of hypergraphs requiring each hyperedge to have a color which appears only on one vertex. More generally, for a positive integer kk there are kk-conflict-free colorings (kk-CF-colorings for short) and kk-strong-conflict-free colorings (kk-SCF-colorings for short). Let HnHn be the hypergraph of which the vertex-set is Vn={1,2,…,n}Vn={1,2,…,n} and the hyperedge-set EnEn is the set of all (non-empty) subsets of VnVn consisting of consecutive elements of VnVn. Firstly, we study the kk-SCF-coloring of HnHn, give the exact kk-SCF-coloring chromatic number of HnHn for k=2,3k=2,3, and present upper and lower bounds of the kk-SCF-coloring chromatic number of HnHn for all kk. Secondly, we give the exact kk-CF-coloring chromatic number of HnHn for all kk.
['Zhen Cui', 'Z. Hu']
On variants of conflict-free-coloring for hypergraphs