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\iteman{io-port 06378529}
\itemau{Li, Yu-Shuang; Zhang, Hua-Jun}
\itemti{Erd\"os-Ko-Rado theorem for ladder graphs.}
\itemso{Acta Math. Appl. Sin., Engl. Ser. 30, No. 3, 583-588 (2014).}
\itemab
Summary: For a graph $G$ and an integer $r \geq 1$, $G$ is $r$-EKR if no intersecting family of independent $r$-sets of $G$ is larger than the largest star (a family of independent $r$-sets containing some fixed vertex in $G$), and $G$ is strictly $r$-EKR if every extremal intersecting family of independent $r$-sets is a star. Recently, {\it G. Hurlbert} and {\it V. Kamat} [J. Comb. Theory, Ser. A 118, No. 3, 829--841 (2011; Zbl 1238.05219)] gave a preliminary result about EKR property of ladder graphs. They showed that a ladder graph with $n$ rungs is 3-EKR for all $n \geq 3$. The present paper proves that this graph is $r$-EKR for all $1 \leq r \leq n$, and strictly $r$-EKR except for $r = n - 1$.
\itemrv{~}
\itemcc{}
\itemut{Erd\H{o}s-Ko-Rado (EKR) theorem; intersecting family; ladder graph}
\itemli{doi:10.1007/s10255-014-0404-x}
\end