Zsolt Tuza:
Combinatorial Batch Codes
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Let n,m,k be given positive integers. We consider multihypergraphs
(i.e., multiple edges are allowed) with n vertices and m edges, with
the property that the union of any i edges contains at least i
vertices, for all i=1,2,...,k. The problem is to minimize the total
size of edges (which is equal to the degree sum). For r fixed, an
interesting related Turan-type problem is to determine the largest m
admitting an r-uniform (multi)hypergraph of order n that satisfies
the condition above with a given k.
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joint work with Csilla Bujtas