We study the intersecting family process initially studied in [Electron. J. Comb., 10:#R29 (2003)]. 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 $k\gg n^{1/2}$.
@article{10_37236_12060,
author = {Alan Frieze and Patrick Bennett and Andrew Newman and Wesley Pegden},
title = {On the intersecting family process},
journal = {The electronic journal of combinatorics},
year = {2024},
volume = {31},
number = {4},
doi = {10.37236/12060},
zbl = {1551.05395},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12060/}
}
TY - JOUR
AU - Alan Frieze
AU - Patrick Bennett
AU - Andrew Newman
AU - Wesley Pegden
TI - On the intersecting family process
JO - The electronic journal of combinatorics
PY - 2024
VL - 31
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/12060/
DO - 10.37236/12060
ID - 10_37236_12060
ER -
%0 Journal Article
%A Alan Frieze
%A Patrick Bennett
%A Andrew Newman
%A Wesley Pegden
%T On the intersecting family process
%J The electronic journal of combinatorics
%D 2024
%V 31
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/12060/
%R 10.37236/12060
%F 10_37236_12060
Alan Frieze; Patrick Bennett; Andrew Newman; Wesley Pegden. On the intersecting family process. The electronic journal of combinatorics, Tome 31 (2024) no. 4. doi: 10.37236/12060
