Intersecting and cross-intersecting families usually appear in extremal combinatorics in the vein of the Erd{ \H o}s--Ko--Rado theorem. On the other hand, P.~Erd{ \H o}s and L.~Lov{ \'a}sz in the noted paper~\cite{ EL} posed problems on coloring intersecting families as a restriction of classical hypergraph coloring problems to a special class of hypergraphs. This note deals with the mentioned coloring problems stated for cross-intersecting families.
Categories: math.CO