Coloring 2-intersecting hypergraphs

Abstract

hypergraph is 2-intersecting if any two edges intersect in at least two vertices. Blais, Weinstein and Yoshida asked (as a FIrst step to a more general problem) whether every 2-intersecting hypergraph has a vertex coloring with a constant number of colors so that each hyperedge has at least min{|e| 3} colors. We show that there is such a coloring with at most 5 colors (which is best possible).