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Mathematics > Combinatorics
Title: On the intersecting family process
(Submitted on 17 Feb 2023 (v1), last revised 9 Mar 2024 (this version, v2))
Abstract: We study the intersecting family process initially studied in \cite{BCFMR}. Here $k=k(n)$ and $E_1,E_2,\ldots,E_m$ is a random sequence of $k$-sets from $\binom{[n]}{k}$ where $E_{r+1}$ is uniformly chosen from those $k$-sets that are not already chosen and that meet $E_i,i=1,2,\ldots,r$. We prove some new results for the case where $k=cn^{1/3}$ and for the case where $k\gg n^{1/2}$.
Submission history
From: Alan Frieze [view email][v1] Fri, 17 Feb 2023 18:28:59 GMT (22kb,D)
[v2] Sat, 9 Mar 2024 16:15:57 GMT (23kb,D)
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