TY  - JOUR
ID  - Katona2017
LB  - Katona2017
AU  - Katona, Gyula O. H.
TI  - A general 2-part Erdȍs-Ko-Rado theorem
ST  - A general 2-part Erdȍs-Ko-Rado theorem
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2017
VL  - 37
IS  - 4
SP  - 577
EP  - 588
DO  - http://dx.doi.org/10.7494/OpMath.2017.37.4.577
UR  - http://dx.doi.org/10.7494/OpMath.2017.37.4.577
AB  - 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.
KW  - extremal set theory
KW  - two-part problem
KW  - intersecting family
SN  - 1232-9274
ER  -