Publikace na Matematicko-fyzikální fakulta |
2017
Abstrakt
We investigate the asymptotic version of the Erdos-Ko-Rado theorem for the random k-uniform hypergraph H-k(n, p). For 2 infinity, the largest intersecting subhypergraph of Hk( n, p) has size (1+o(1))p(n)(k)-N for any p >> n/k ln(2) (n/k) D-1.
This lower bound on p is asymptotically best possible for k = Theta(n). For this range of k and p, we are able to show stability as well.
A different behaviour occurs when k = o(n). In this case, the lower bound on p is almost optimal.
Further, for the small interval D-1 > root nlnn. Together with previous work of Balogh, Bohman and Mubayi, these results settle the asymptotic size of the largest intersecting family in H-k(n, p), for essentially all values of p and k.