Hong Liu

A Near-Optimal Linear Range for the Erd\H{o}s Matching Conjecture

The Erd\H{o}s Matching Conjecture is governed by two competing ways of excluding $s+1$ disjoint edges: one may concentrate all edges on fewer than $k(s+1)$ vertices, or force every edge to meet a fixed $s$-set. We determine a near-optimal range in which the second construction is extremal. For every fixed $k\ge2$, ther...