## 20 Citations

### Short proofs of some extremal results III

- MathematicsRandom Struct. Algorithms
- 2020

We prove a selection of results from different areas of extremal combinatorics, including complete or partial solutions to a number of open problems. These results, coming mainly from extremal graph…

### C O ] 1 8 O ct 2 01 9 Short proofs of some extremal results III

- Mathematics
- 2019

We prove a selection of results from different areas of extremal combinatorics, including complete or partial solutions to a number of open problems. These results, coming mainly from extremal graph…

### Recent developments in graph Ramsey theory

- MathematicsSurveys in Combinatorics
- 2015

There has been a great deal of recent progress on the study of Ramsey numbers and their variants, spurred on by the many advances across extremal combinatorics.

### Existence of Spanning ℱ-Free Subgraphs with Large Minimum Degree

- MathematicsCombinatorics, Probability and Computing
- 2016

Here the asymptotically tight results for many families of bipartite graphs such as cycles or complete bipartites graphs are provided.

### A remark on the Ramsey number of the hypercube

- Mathematics, Computer Science
- 2022

This paper shows that r ( Q n ) = O (2 2 n − cn ) for a universal constant c > 0.

### Maximum H-free subgraphs

- Mathematics
- 2019

Given a family of hypergraphs H, let f(m,H) denote the largest size of an H-free subgraph that one is guaranteed to find in every hypergraph with m edges. This function was first introduced by Erdős…

### Tiling with monochromatic bipartite graphs of bounded maximum degree

- Mathematics
- 2021

We prove that for any r ∈ N, there exists a constant Cr such that the following is true. Let F = {F1, F2, . . . } be an infinite sequence of bipartite graphs such that |V (Fi)| = i and ∆(Fi) ≤ ∆ hold…

### Ramsey numbers of degenerate graphs

- Mathematics
- 2015

A graph is $d$-degenerate if all its subgraphs have a vertex of degree at most $d$. We prove that there exists a constant $c$ such that for all natural numbers $d$ and $r$, every $d$-degenerate graph…

### Ramsey numbers of sparse digraphs

- Mathematics
- 2021

Burr and Erdős in 1975 conjectured, and Chvátal, Rödl, Szemerédi and Trotter later proved, that the Ramsey number of any bounded degree graph is linear in the number of vertices. In this paper, we…

## References

SHOWING 1-10 OF 151 REFERENCES

### Short Proofs of Some Extremal Results

- MathematicsCombinatorics, Probability and Computing
- 2013

These results, coming from areas such as extremal graph theory, Ramsey theory and additive combinatorics, have been collected together because each case the relevant proofs are quite short.

### Regular Partitions of Graphs

- Mathematics
- 1975

Abstract : A crucial lemma in recent work of the author (showing that k-term arithmetic progression-free sets of integers must have density zero) stated (approximately) that any large bipartite graph…

### A New Lower Bound For A Ramsey-Type Problem

- MathematicsComb.
- 2005

A new lower bound on the size of the maximum subset of G without a copy of complete graph Kr is provided to substantially improve previous bounds of Krivelevich and Bollobás and Hind.

### Note on a Generalization of Roth’s Theorem

- Mathematics
- 2003

We give a simple proof that for sufficiently large N, every subset of of size[N 2]of size at least δN 2 contains three points of the form (a,b), (a + d, b), (a, b + d).

### Problems and results in Extremal Combinatorics – III

- Mathematics
- 2016

Extremal Combinatorics is one of the most active topics in Discrete Mathematics, dealing with problems that are often motivated by questions in other areas, including Theoretical Computer Science,…

### A Disproof of a Conjecture of Erdős in Ramsey Theory

- Mathematics
- 1989

Contre-exemples a la conjecture de Erdos et discussion des proprietes des graphes extremaux

### Ks-Free Graphs Without Large Kr-Free Subgraphs

- MathematicsCombinatorics, Probability and Computing
- 1994

It is shown that for every 2 ≤ r s , and n sufficiently large, there exist graphs of order n, not containing a complete graph on s vertices, in which every relatively not too small subset of vertices spans a completegraph on r vertices.