Classification of Maximum Hittings by Large Families

Abstract

For integers r and n, where n is sufficiently large, and for every set X ⊆ [n] we determine the maximal left-compressed intersecting families A ⊆ [n] r which achieve maximum hitting with X (i.e. have the most members which intersect X). This answers a question of Barber, who extended previous results by Borg to characterise those sets X for which maximum hitting is achieved by the star.