Paul Brooks

Extreme Tornados: r-Partite Intersecting Hypergraphs with Covering Number r-1

Abstract: K\"{o}nig's Theorem states that the covering number τ equals the matching number ν in bipartite graphs. Ryser's conjecture asserts that for r-partite hypergraphs, τ <= (r-1)ν. The conjecture is also open for intersecting hypergraphs; i.e., for hypergraphs where ν = 1, τ <= r-1. An intersecting hypergraph with τ = r-1 must contain a structure called a tornado. Properties of tornados with covering number r-1 are described. The talk begins with a motivation of the study of hypergraphs as a way to understand metabolic reaction networks in living cells.