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 2021Show all

8 papers · 1 filter

math.CO2021

Solution to a problem of Erdős on the chromatic index of hypergraphs with bounded codegree

Dong Yeap Kang, Tom Kelly, Daniela Kühn +2

In 1977, Erdős asked the following question: for any integers $t, n \in N$ , if $G_{1}, \dots, G_{n}$ are complete graphs such that each $G_{i}$ has at most $n$ vertices and eve…

math.CO2021

Counting cliques in $1$ -planar graphs

J. Pascal Gollin, Kevin Hendrey, Abhishek Methuku +2

The problem of maximising the number of cliques among $n$ -vertex graphs from various graph classes has received considerable attention. We investigate this problem for the class of…

math.CO2021

Rainbow subdivisions of cliques

Tao Jiang, Shoham Letzter, Abhishek Methuku +1

We show that for every integer $m \geq 2$ and large $n$ , every properly edge-coloured graph on $n$ vertices with at least $n (lo g n)^{53}$ edges contains a rainbow subdivision of $…

math.CO2021★ 10 cited

Rainbow Turán number of clique subdivisions

Tao Jiang, Abhishek Methuku, Liana Yepremyan

We show that for any integer $t \geq 2$ , every properly edge-coloured graph on $n$ vertices with more than $n^{1 + o (1)}$ edges contains a rainbow subdivision of $K_{t}$ . Note that this…

math.CO2021★ 3 cited

Graph and hypergraph colouring via nibble methods: A survey

Dong Yeap Kang, Tom Kelly, Daniela Kühn +2

This paper provides a survey of methods, results, and open problems on graph and hypergraph colourings, with a particular emphasis on semi-random `nibble' methods. We also give a d…

math.CO2021

Ramsey numbers of Boolean lattices

Dániel Grósz, Abhishek Methuku, Casey Tompkins

The poset Ramsey number $R (Q_{m}, Q_{n})$ is the smallest integer $N$ such that any blue-red coloring of the elements of the Boolean lattice $Q_{N}$ has a blue induced copy of $Q_{m}$ or a…

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.CO2021★ 2 cited

A proof of the Erdős-Faber-Lovász conjecture

Dong Yeap Kang, Tom Kelly, Daniela Kühn +2

The Erdős-Faber-Lovász conjecture (posed in 1972) states that the chromatic index of any linear hypergraph on $n$ vertices is at most $n$ . In this paper, we prove this conjecture f…

Solution to a problem of Erdős on the chromatic index of hypergraphs with bounded codegree

Counting cliques in 1-planar graphs

Rainbow subdivisions of cliques

Rainbow Turán number of clique subdivisions

Graph and hypergraph colouring via nibble methods: A survey

Ramsey numbers of Boolean lattices

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

A proof of the Erdős-Faber-Lovász conjecture

Counting cliques in $1$ -planar graphs

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