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Fundamentalnaya i Prikladnaya Matematika, 2020, Volume 23, Issue 1, Pages 95–122
(Mi fpm1869)
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This article is cited in 2 scientific papers (total in 2 papers)
On some generalizations of the property B problem of an $n$-uniform hypergraph
Yu. A. Demidovich Moscow Institute of Physics and Technology, Moscow, Russia
Abstract:
The extremal problem of hypergraph colorings related to the Erdős–Hajnal property $B$-problem is considered. Let $k$ be a natural number. The problem is to find the value of $m_k(n)$ equal to the minimal number of edges in an $n$-uniform hypergraph that does not admit $2$-colorings of the vertex set such that every edge of the hypergraph contains at least $k$ vertices of each color. In this paper, we obtain new lower bounds for $m_k(n)$.
Citation:
Yu. A. Demidovich, “On some generalizations of the property B problem of an $n$-uniform hypergraph”, Fundam. Prikl. Mat., 23:1 (2020), 95–122; J. Math. Sci., 262:4 (2022), 457–475
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https://www.mathnet.ru/eng/fpm1869 https://www.mathnet.ru/eng/fpm/v23/i1/p95
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Abstract page: | 187 | Full-text PDF : | 57 | References: | 16 |
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