Geodesic
New lower bound for the minimal number of edges of simple uniform hypergraph without the property $B_k$
Diskretnaya Matematika, Tome 32 (2020) no. 4, pp. 10-37

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A hypergraph $H=(V,E)$ has the property $B_k$ if there exists an assignment of two colors to $V$ such that each edge contains at least $k$ vertices of each color. A hypergraph is called simple if every two edges of it have at most one common vertex. We obtain a new lower bound for the minimal number of edges of $n$-uniform simple hypergraph without the property $B_k$.
Keywords: simple hypergraphs, colorings of hypergraphs, property $B$. 
@article{DM_2020_32_4_a1,
     author = {Yu. A. Demidovich},
     title = {New lower bound for the minimal number of edges of simple uniform hypergraph without the property $B_k$},
     journal = {Diskretnaya Matematika},
     pages = {10--37},
     publisher = {mathdoc},
     volume = {32},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2020_32_4_a1/}
}
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Yu. A. Demidovich. New lower bound for the minimal number of edges of simple uniform hypergraph without the property $B_k$. Diskretnaya Matematika, Tome 32 (2020) no. 4, pp. 10-37. http://geodesic.mathdoc.fr/item/DM_2020_32_4_a1/