On some generalizations of the property $B$-problem of an $n$-uniform hypergraph

Yury Demidovich

On some generalizations of the property $B$-problem of an $n$-uniform hypergraph

Combinatorics 2019-03-29 v1

Authors: Yury Demidovich

Abstract

The extremal problem of hypergraph colorings related to Erd\H{o}s--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 not admitting $2$ -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 $m_k(n).$

Keywords

hypergraph coloring property B extremal problem n-uniform hypergraph lower bounds

Cite

@article{arxiv.1903.11708,
  title  = {On some generalizations of the property $B$-problem of an $n$-uniform hypergraph},
  author = {Yury Demidovich},
  journal= {arXiv preprint arXiv:1903.11708},
  year   = {2019}
}

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