Geodesic
Systems of Representatives
Matematičeskie zametki, Tome 106 (2019) no. 3, pp. 387-394

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Lower and upper bounds are obtained for the size $\zeta(n,r,s,k)$ of a minimum system of common representatives for a system of families of $k$-element sets. By $\zeta(n,r,s,k)$ we mean the maximum (over all systems $\Sigma=\{M_1,\dots,M_r\}$ of sets $M_i$ consisting of at least $s$ subsets of $\{1,\dots,n\}$ of cardinality not exceeding $k$) of the minimum size of a system of common representatives of $\Sigma$. The obtained results generalize previous estimates of $\zeta(n,r,s,1)$.
Keywords: systems of common representatives, minimum systems of common representatives. 
@article{MZM_2019_106_3_a5,
     author = {K. D. Kovalenko and A. M. Raigorodskii},
     title = {Systems of {Representatives}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {387--394},
     publisher = {mathdoc},
     volume = {106},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_106_3_a5/}
}
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K. D. Kovalenko; A. M. Raigorodskii. Systems of Representatives. Matematičeskie zametki, Tome 106 (2019) no. 3, pp. 387-394. http://geodesic.mathdoc.fr/item/MZM_2019_106_3_a5/