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                * Princeton Discrete Math Seminar *
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Date: Thursday 22 September, 2.15 in Fine Hall 224
 
Speaker: Ron Aharoni, Technion, Haifa

Title: Erdos-Ko-Rado-like theorems for rainbow matchings.

Let f(n,k,r) be the smallest number such that every set of more than
f(n,k,r) r-sets in [n] contains a matching of size k. The Erdos-Ko-Rado
theorem states that f(n,2,r)=\binom{n-1}{r-1}. A natural conjecture is 
that if F_1, F_2, ...F_k \subseteq \binom{[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 (Matsumoto-Tokushige) 
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.


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Next week:  Benny Sudakov

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