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\iteman{io-port 05175296}
\itemau{Mubayi, Dhruv; Verstra\"ete, Jacques}
\itemti{Minimal paths and cycles in set systems.}
\itemso{Eur. J. Comb. 28, No. 6, 1681-1693 (2007).}
\itemab
A family of sets $A_0,\dots,A_{k-1}$ form a minimal $k$-cycle if $A_i\cap A_j \ne \emptyset$ if and only if $(i=j$ or these two are consecutive modulo $k).$ Denote $f_r(n,k)$ the maximum size of a family of $r$-sets of an $n$-element underlying set, not containing minimal $k$-cycle. The paper determines new lower and upper bounds for this value. The proofs are based on classical extremal set theoretical results of Paul Erd\H{o}s and others.
\itemrv{P\'eter L. Erd\H os (Budapest)}
\itemcc{}
\itemut{minimal cycle; minimal path; Erd\H{o}s-Ko-Rado theorem}
\itemli{doi:10.1016/j.ejc.2006.07.001}
\end