On the Intersecting Family Process - Frieze, Alan; Bennett, Patrick; Newman, Andrew; Pegden, Wesley (The Electronic Journal of Combinatorics, 2024)
We study the intersecting family process initially studied in [Electron. J. Comb., 10:#R29 (2003)]. Here k=k(n) and E_1,E_2,…,E_m is a random sequence of k-sets from [n]k where E_r+1 is uniformly chosen from those k-sets that are not already chosen and that meet E_i,i=1,2,…,r. We prove some new results for the case where k=cn^1/3 and for the case where kn^1/2.