ErdosKoRadolike theorems for rainbow matchings
ErdosKoRadolike theorems for rainbow matchings

Ron Aharoni, Technion, Haifa
Fine Hall 224
Let $f(n,k,r)$ be the smallest number such that every set of more than $f(n,k,r)$ rsets in $[n]$ contains a matching of size $k$. The ErdosKoRado theorem states that $f(n,2,r)=(n1)(r1)$. A natural conjecture is that if $F_1, F_2, ...F_k \subseteq {[n]}{r}$ are all of size larger than $f(n,k,r)$ then they possess a rainbow matching, that is, a choice of disjoint edges, one from each $F_i$. This is known for $k=2$ (MatsumotoTokushige) and $r=2$ (Meshulam). We consider the analogue of this conjecture in $r$partite hypergraphs, and prove the cases $r=3$ and $k=2$.Joint work with David Howard.