Beka Ergemlidze

activity

20162021

most citedTurán number of an induced complete bipartite graph plus an odd cycle

5 citations · 11 across the 11 of their papers we have counts for

collaborators

14 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★ 1 cited

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…

math.CO2019

$3$ -uniform hypergraphs without a cycle of length five

Beka Ergemlidze, Ervin Győri, Abhishek Methuku

In this paper we show that the maximum number of hyperedges in a $3$ -uniform hypergraph on $n$ vertices without a (Berge) cycle of length five is less than $(0.254 + o (1)) n^{3/2}$ ,…

math.CO2018

Triangles in $C_{5}$ -free graphs and Hypergraphs of Girth Six

Beka Ergemlidze, Abhishek Methuku

We introduce a new approach and prove that the maximum number of triangles in a $C_{5}$ -free graph on $n$ vertices is at most $(1 + o (1)) \frac{1}{3 2} n^{3/2} .$ We also show…

math.CO2018

On the Rainbow Turán number of paths

Beka Ergemlidze, Ervin Győri, Abhishek Methuku

Let $F$ be a fixed graph. The rainbow Turán number of $F$ is defined as the maximum number of edges in a graph on $n$ vertices that has a proper edge-coloring with no rainbow copy…

math.CO2017★ 5 cited

Turán number of an induced complete bipartite graph plus an odd cycle

Beka Ergemlidze, Ervin Győri, Abhishek Methuku

Let $k \geq 2$ be an integer. We show that if $s = 2$ and $t \geq 2$ , or $s = t = 3$ , then the maximum possible number of edges in a $C_{2 k + 1}$ -free graph containing no induced copy…

math.CO2017

A note on the maximum number of triangles in a $C_{5}$ -free graph

Beka Ergemlidze, Ervin Győri, Abhishek Methuku +1

We prove that the maximum number of triangles in a $C_{5}$ -free graph on $n$ vertices is at most $\frac{1}{2 2} (1 + o (1)) n^{3/2}$ , improving an estimate of Alon and Shikhelma…

math.CO2017

Asymptotics for Turán numbers of cycles in 3-uniform linear hypergraphs

Beka Ergemlidze, Ervin Győri, Abhishek Methuku

Let $F$ be a family of $3$ -uniform linear hypergraphs. The linear Turán number of $F$ is the maximum possible number of edges in a $3$ -uniform linear hypergraph…

math.CO2016

On the Linear Cycle Cover Conjecture of Gyárfás and Sárközy

Beka Ergemlidze, Ervin Győri, Abhishek Methuku

A linear cycle in a hypergraph $H$ is a cyclic sequence of hyperedges such that two consecutive hyperedges intersect in exactly one element and two nonconsecutive hyperedges are di…

math.CO2016

$3$ -uniform hypergraphs and linear cycles

Beka Ergemlidze, Ervin Győri, Abhishek Methuku

Gyárfás, Győri and Simonovits proved that if a $3$ -uniform hypergraph with $n$ vertices has no linear cycles, then its independence number $α \geq \frac{2 n}{5}$ . The hypergraph cons…

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

The exact linear Turán number of the Sail

A note on maximum size of Berge-C4​-free hypergraphs

New bounds for a hypergraph Bipartite Turán problem

3-uniform hypergraphs without a cycle of length five

Triangles in C5​-free graphs and Hypergraphs of Girth Six

On the Rainbow Turán number of paths

Turán number of an induced complete bipartite graph plus an odd cycle

A note on the maximum number of triangles in a C5​-free graph

Asymptotics for Turán numbers of cycles in 3-uniform linear hypergraphs

On the Linear Cycle Cover Conjecture of Gyárfás and Sárközy

3-uniform hypergraphs and linear cycles

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

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

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

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

$3$ -uniform hypergraphs without a cycle of length five

Triangles in $C_{5}$ -free graphs and Hypergraphs of Girth Six

A note on the maximum number of triangles in a $C_{5}$ -free graph

$3$ -uniform hypergraphs and linear cycles