On Some Generalizations of the Property B Problem of an n-Uniform Hypergraph

Yu A. Demidovich

doi:10.1007/s10958-022-05828-6

On Some Generalizations of the Property B Problem of an n-Uniform Hypergraph

Yu A. Demidovich^*

^*Corresponding author for this work

Computer Science

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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).

Original language	English (US)
Pages (from-to)	457-475
Number of pages	19
Journal	Journal of Mathematical Sciences (United States)
Volume	262
Issue number	4
DOIs	https://doi.org/10.1007/s10958-022-05828-6
State	Published - Apr 2022

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Applied Mathematics

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abstract = "The extremal problem of hypergraph colorings related to the Erd{\H o}s–Hajnal property B-problem is considered. Let k be a natural number. The problem is to find the value of mk(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 mk(n).",

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On Some Generalizations of the Property B Problem of an n-Uniform Hypergraph

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