## 35 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…

Color‐biased Hamilton cycles in random graphs

- MathematicsRandom Struct. Algorithms
- 2022

We prove that a random graph G(n,p) , with p above the Hamiltonicity threshold, is typically such that for any r‐coloring of its edges there exists a Hamilton cycle with at least (2/(r+1)−o(1))n…

A short nonalgorithmic proof of the containers theorem for hypergraphs

- MathematicsProceedings of the American Mathematical Society
- 2019

Recently the breakthrough method of hypergraph containers, developed independently by Balogh, Morris, and Samotij as well as Saxton and Thomason, has been used to study sparse random analogues of a…

Dirac's theorem for random graphs

- Mathematics, Computer ScienceRandom Struct. Algorithms
- 2012

Motivated by the study of resilience of random graph properties, it is proved that if p ≫ log n/n, then a.s. every subgraph of G(n,p) with minimum degree at least (1/2 + o (1) )np is Hamiltonian.

Structure and randomness in extremal combinatorics

- Mathematics
- 2017

In this thesis we prove several results in extremal combinatorics from areas including Ramsey theory, random graphs and graph saturation. We give a random graph analogue of the classical Andr´asfai,…

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The Green-Tao theorem: an exposition

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The celebrated Green-Tao theorem states that the prime numbers contain arbitrarily long arithmetic progressions. We give an exposition of the proof, incorporating several simplifications that have…

Randomness and regularity

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Regularity Lemmas for Graphs

- Mathematics
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Szemeredi’s regularity lemma proved to be a fundamental result in modern graph theory. It had a number of important applications and is a widely used tool in extremal combinatorics. For some further…

Turán's theorem in sparse random graphs

- MathematicsRandom Struct. Algorithms
- 2003

It is shown that with probability 1 - o(1), one needs to delete approximately 1/k-1-fraction of the edges in a random graph in order to destroy all cliques of size k.

A new proof of Szemerédi's theorem

- Mathematics
- 2001

In 1927 van der Waerden published his celebrated theorem on arithmetic progressions, which states that if the positive integers are partitioned into finitely many classes, then at least one of these…