Csilla Bujtas: Partition-crossing hypergraphs
Source: Discrete mathematics seminar
The problem of determining these minimum values for k=r was raised and studied by several authors, first by Sterboul in 1973. In an earlier research, we determined asymptotically tight estimates on f(n,k,k) for every fixed k as n → ∞. Now we consider the more general problem and establish lower and upper bounds for f(n,k,r). For various combinations of the three values n,k,r we obtain asymptotically tight estimates, and also point out close connections of the function f(n,k,r) to Turán-type extremal problems on graphs and hypergraphs.