@Article{Katona2017,
author = "Katona, Gyula O. H.",
title = "A general 2-part Erdȍs-Ko-Rado theorem",
journal = "Opuscula Math.",
year = "2017",
volume = "37",
number = "4",
pages = "577--588",
doi = "http://dx.doi.org/10.7494/OpMath.2017.37.4.577",
url = "http://dx.doi.org/10.7494/OpMath.2017.37.4.577",
abstract = "A two-part extension of the famous Erdȍs-Ko-Rado Theorem is proved. The underlying set is partitioned into \(X_1\) and \(X_2\). Some positive integers \(k_i\), \(\ell_i\) (\(1\leq i\leq m\)) are given. We prove that if \(\mathcal{F}\)) is an intersecting family containing members \(F\) such that \(|F\cap X_1|=k_i\), \(|F\cap X_2|=\ell_i\) holds for one of the values \(i\) (\(1\leq i\leq m\)) then \(|\mathcal{F}|\) cannot exceed the size of the largest subfamily containing one element.",
keywords = "extremal set theory, two-part problem, intersecting family",
issn = "1232-9274"
}