| Autor: |
Akhmejanova, Margarita, Shabanov, Dmitry |
| Rok vydání: |
2019 |
| Předmět: |
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| Zdroj: |
\emph{Discrete Applied Mathematics}, (2019), https://doi.org/10.1016/j.dam.2019.03.024 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1016/j.dam.2019.03.024 |
| Popis: |
The paper deals with an extremal problem concerning equitable colorings of uniform hyper\-graph. Recall that a vertex coloring of a hypergraph $H$ is called proper if there are no monochro-matic edges under this coloring. A hypergraph is said to be equitably $r$-colorable if there is a proper coloring with $r$ colors such that the sizes of any two color classes differ by at most one. In the present paper we prove that if the number of edges $|E(H)|\leq 0.01\left(\frac{n}{\ln n}\right)^{\frac {r-1}{r}}r^{n-1}$ then the hypergraph $H$ is equitably $r$-colorable provided $r<\sqrt[5]{\ln n}$. |
| Databáze: |
arXiv |
| Externí odkaz: |
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