New lower bound for the minimal number of edges of simple uniform hypergraph without the property Bk

Yury A. Demidovich

doi:10.1515/dma-2022-0015

New lower bound for the minimal number of edges of simple uniform hypergraph without the property B_k

Yury A. Demidovich^*

^*Corresponding author for this work

Computer Science

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

Abstract

A hypergraph H = (V, E) has the property Bk 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 Bk.

Original language	English (US)
Pages (from-to)	155-176
Number of pages	22
Journal	Discrete Mathematics and Applications
Volume	32
Issue number	3
DOIs	https://doi.org/10.1515/dma-2022-0015
State	Published - Jun 1 2022

Keywords

colorings of hypergraphs
property B
simple hypergraphs

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.1515/dma-2022-0015

Cite this

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abstract = "A hypergraph H = (V, E) has the property Bk 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 Bk.",

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note = "Funding Information: Funding : The reported study was funded by RFBR, project number 19-31-90016. Publisher Copyright: {\textcopyright} 2022 Walter de Gruyter GmbH, Berlin/Boston.",

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