Bollobás-type inequalities on set $k$-tuples

Jason O'Neill, Jacques Verstraete

Published 2018-12-03Version 1

The Bollob\'as set pairs inequality is a fundamental result in extremal set theory. In this paper, we examine suitable conditions on $k$-wise intersections from a $k$-tuple of set families for which a Bollob\'as-type inequality holds. We then use the standard connection between extremal set theory and covering problems to give lower and upper bounds on the biclique covering numbers of a few particular $k$-uniform hypergraphs. We also provide random and explicit constructions of these Bollob\'as set $k$-tuples.