Abhishek Methuku

activity

20142026

most citedAn Erdős-Gallai type theorem for uniform hypergraphs

39 citations · 146 across the 54 of their papers we have counts for

collaborators

Showing 2017Show all

13 papers · 1 filter

math.CO2017★ 1 cited

Generalized Turán problems for even cycles

Dániel Gerbner, Ervin Győri, Abhishek Methuku +1

Given a graph $H$ and a set of graphs $F$ , let $e x (n, H, F)$ denote the maximum possible number of copies of $H$ in an $F$ -free graph on $n$ vertices. We i…

math.CO2017★ 1 cited

Generalized Turán problems for disjoint copies of graphs

Dániel Gerbner, Abhishek Methuku, Máté Vizer

Given two graphs $H$ and $F$ , the maximum possible number of copies of $H$ in an $F$ -free graph on $n$ vertices is denoted by $e x (n, H, F)$ . We investigate the function $e x (n, H, k F)$ ,…

math.CO2017

Forbidding rank-preserving copies of a poset

Dániel Gerbner, Abhishek Methuku, Dániel T. Nagy +2

The maximum size, $L a (n, P)$ , of a family of subsets of $[n] = {1, 2, ..., n}$ without containing a copy of $P$ as a subposet, has been intensively studied. Let $P$ be a graded poset.…

math.CO2017

On the maximum size of connected hypergraphs without a path of given length

Ervin Győri, Abhishek Methuku, Nika Salia +2

In this note we asymptotically determine the maximum number of hyperedges possible in an $r$ -uniform, connected $n$ -vertex hypergraph without a Berge path of length $k$ , as $n$ and…

math.CO2017

Saturation of Berge Hypergraphs

Sean English, Nathan Graber, Pamela Kirkpatrick +2

Given a graph $F$ , a hypergraph is a Berge- $F$ if it can be obtained by expanding each edge in $F$ to a hyperedge containing it. A hypergraph $H$ is Berge- $F$ -saturated if $H$ does…

math.CO2017★ 10 cited

On the Turán number of some ordered even cycles

Ervin Győri, Dániel Korándi, Abhishek Methuku +3

A classical result of Bondy and Simonovits in extremal graph theory states that if a graph on $n$ vertices contains no cycle of length $2 k$ then it has at most $O (n^{1 + 1/ k})$ edges…

math.CO2017★ 3 cited

A simple discharging method for forbidden subposet problems

Ryan R. Martin, Abhishek Methuku, Andrew Uzzell +1

The poset $Y_{k + 1, 2}$ consists of $k + 2$ distinct elements $x_{1}$ , $x_{2}$ , \dots, $x_{k}$ , $y_{1}$ , $y_{2}$ , such that $x_{1} \leq x_{2} \leq \dots \leq x_{k} \leq y_{1}$ ,~ $y_{2}$ . The poset $Y'_{k+1…

math.CO2017★ 1 cited

An improvement on the maximum number of $k$ -Dominating Independent Sets

Dániel Gerbner, Balázs Keszegh, Abhishek Methuku +2

Erdős and Moser raised the question of determining the maximum number of maximal cliques or equivalently, the maximum number of maximal independent sets in a graph on $n$ vertices.…

math.CO2017★ 1 cited

On subgraphs of $C_{2 k}$ -free graphs and a problem of Kühn and Osthus

Dániel Grósz, Abhishek Methuku, Casey Tompkins

Let $c$ denote the largest constant such that every $C_{6}$ -free graph $G$ contains a bipartite and $C_{4}$ -free subgraph having $c$ fraction of edges of $G$ . Győri et al. showed tha…

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★ 3 cited

Asymptotics for the Turán number of Berge- $K_{2, t}$

Dániel Gerbner, Abhishek Methuku, Máté Vizer

Let $F$ be a graph. A hypergraph is called Berge- $F$ if it can be obtained by replacing each edge of $F$ by a hyperedge containing it. Let $F$ be a family of graphs. The…

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…

Generalized Turán problems for even cycles

Generalized Turán problems for disjoint copies of graphs

Forbidding rank-preserving copies of a poset

On the maximum size of connected hypergraphs without a path of given length

Saturation of Berge Hypergraphs

On the Turán number of some ordered even cycles

A simple discharging method for forbidden subposet problems

An improvement on the maximum number of k-Dominating Independent Sets

On subgraphs of C2k​-free graphs and a problem of Kühn and Osthus

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 the Turán number of Berge-K2,t​

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

An improvement on the maximum number of $k$ -Dominating Independent Sets

On subgraphs of $C_{2 k}$ -free graphs and a problem of Kühn and Osthus

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

Asymptotics for the Turán number of Berge- $K_{2, t}$