Let F be a triple system on an n element set. Suppose that F contains more than (1/3 - epsilon) (n3) triples, where epsilon > 10(-6) is explicitly defined and n is sufficiently large. Then there is a set of four points containing at least three triples of F. This improves previous bounds of de Caen [1] and Matthias [7].
机构:
Alfred Renyi Inst Math, Budapest, Hungary
MTA ELTE Lendulet Combinatorial Geometry Res Grp, Budapest, HungaryAlfred Renyi Inst Math, Budapest, Hungary