Spanning (2-)trees of intersection graphs and hunter-worsley-type set bounds

Abstract

The Hunter-Worsley inequality is an upper bound on the cardinality of the union of sets in terms of the cardinalities of the individual sets and some of their pairwise-intersections. This is a simple application of spanning trees of intersection graphs to probability theory. I propose an alternative bound similarly based on spanning 2-trees - definable recursively from K ₂ as trees are, except by attaching new triangles to previously-existing edges, instead of new edges to previously-existing vertices - and I defend this bound as- being the proper 2-tree analog of the Hunter-Worsley bound.