Beka Ergemlidze

activity

20172021

most citedOn

3

-uniform hypergraphs avoiding a cycle of length four

2 citations · 5 across the 6 of their papers we have counts for

collaborators

10 papers

math.CO2021★ 1 cited

Transversal $C_{k}$ -factors in subgraphs of the balanced blow-up of $C_{k}$

Beka Ergemlidze, Theodore Molla

For a subgraph $G$ of the blow-up of a graph $F$ , we let $δ^{*} (G)$ be the smallest minimum degree over all of the bipartite subgraphs of $G$ induced by pairs of parts that correspon…

math.CO2021★ 2 cited

Minimizing the number of complete bipartite graphs in a $K_{s}$ -saturated graph

Beka Ergemlidze, Abhishek Methuku, Michael Tait +1

A graph $G$ is $F$ -saturated if it contains no copy of $F$ as a subgraph but the addition of any new edge to $G$ creates a copy of $F$ . We prove that for $s \geq 3$ and $t \geq 2$ ,…

math.CO2020★ 2 cited

On $3$ -uniform hypergraphs avoiding a cycle of length four

Beka Ergemlidze, Ervin Győri, Abhishek Methuku +2

In this note we show that the maximum number of edges in a $3$ -uniform hypergraph without a Berge cycle of length four is at most $(1 + o (1)) \frac{n ^{3/2}}{10}$ . This improves…

math.CO2020

The exact linear Turán number of the Sail

Beka Ergemlidze, Ervin Győri, Abhishek Methuku

A hypergraph is linear if any two of its edges intersect in at most one vertex. The Sail (or $3$ -fan) $F^{3}$ is the $3$ -uniform linear hypergraph consisting of $3$ edges $f_1, f_2,…

math.CO2020

A note on maximum size of Berge- $C_{4}$ -free hypergraphs

Beka Ergemlidze

In this paper, we consider maximum possible value for the sum of cardinalities of hyperedges of a hypergraph without a Berge $4$ -cycle. We significantly improve the previous upper…

math.CO2019

New bounds for a hypergraph Bipartite Turán problem

Beka Ergemlidze, Tao Jiang, Abhishek Methuku

Let $t$ be an integer such that $t \geq 2$ . Let $K_{2, t}^{(3)}$ denote the triple system consisting of the $2 t$ triples ${a, x_{i}, y_{i}}$ , ${b, x_{i}, y_{i}}$ for $1 \leq i \leq t$ , where t…

Transversal Ck​-factors in subgraphs of the balanced blow-up of Ck​

Minimizing the number of complete bipartite graphs in a Ks​-saturated graph

On 3-uniform hypergraphs avoiding a cycle of length four