For integers r and n, where n is sufficiently large, and for every set
Xβ[n] we determine the maximal left-compressed intersecting
families Aβ(r[n]β) 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.Comment: v2: minor corrections in response to reviewer comments. To appear in
Graphs and Combinatoric