Stability analysis for \(k\)-wise intersecting families
The electronic journal of combinatorics, Tome 18 (2011) no. 1
We consider the following generalization of the seminal Erdős–Ko–Rado theorem, due to Frankl. For some $k\geq 2$, let $\mathcal{F}$ be a $k$-wise intersecting family of $r$-subsets of an $n$ element set $X$, i.e. for any $F_1,\ldots,F_k\in \mathcal{F}$, $\cap_{i=1}^k F_i\neq \emptyset$. If $r\leq \dfrac{(k-1)n}{k}$, then $|\mathcal{F}|\leq {n-1 \choose r-1}$. We prove a stability version of this theorem, analogous to similar results of Dinur-Friedgut, Keevash-Mubayi and others for the EKR theorem. The technique we use is a generalization of Katona's circle method, initially employed by Keevash, which uses expansion properties of a particular Cayley graph of the symmetric group.
@article{10_37236_602,
author = {Vikram Kamat},
title = {Stability analysis for \(k\)-wise intersecting families},
journal = {The electronic journal of combinatorics},
year = {2011},
volume = {18},
number = {1},
doi = {10.37236/602},
zbl = {1220.05128},
url = {http://geodesic.mathdoc.fr/articles/10.37236/602/}
}
Vikram Kamat. Stability analysis for \(k\)-wise intersecting families. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/602
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