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- David Conlon
- 2008

We prove a new upper bound for diagonal two-colour Ramsey numbers, showing that there exists a constant C such that r(k + 1, k + 1) ≤ k log k log log k (

- David Conlon, Hiêp Hàn, Yury Person, Mathias Schacht
- Random Struct. Algorithms
- 2012

We study quasi-random properties of k-uniform hypergraphs. Our central notion is uniform edge distribution with respect to large vertex sets. We will find several equivalent characterisations of this… (More)

- David Conlon, Jacob Fox
- ArXiv
- 2011

We show, for any positive integer k, that there exists a graph in which any equitable partition of its vertices into k parts has at least ck/ log∗ k pairs of parts which are not ǫ-regular, where c, ǫ… (More)

- David Conlon, Jacob Fox, Benny Sudakov
- Discrete Applied Mathematics
- 2013

The partition relation N → (n)` means that whenever the k-tuples of an N -element set are `colored, there is a monochromatic set of size n, where a set is called monochromatic if all its k-tuples… (More)

Given a graph H on vertex set {1, 2, · · · , n} and a function f : [0, 1] → R, define ‖f‖H := ∣∣∣∣∣ ∫ ∏ ij∈E(H) f(xi, xj)dμ |V (H)| ∣∣∣∣∣ 1/|E(H)| , where μ is the Lebesgue measure on [0, 1]. We say… (More)

- David Conlon, Jacob Fox, Choongbum Lee, Benny Sudakov
- J. Comb. Theory, Ser. B
- 2017

Given a labeled graph H with vertex set {1, 2, . . . , n}, the ordered Ramsey number r<(H) is the minimum N such that every two-coloring of the edges of the complete graph on {1, 2, . . . , N}… (More)

- David Conlon, Jacob Fox, Benny Sudakov
- Combinatorica
- 2012

The Ramsey number r(H) of a graph H is the least positive integer N such that every two-coloring of the edges of the complete graph KN contains a monochromatic copy of H . A famous result of Chvátal,… (More)

- David Conlon, Jacob Fox
- Surveys in Combinatorics
- 2013

The graph removal lemma states that any graph on n vertices with o(n) copies of a fixed graph H may be made H-free by removing o(n) edges. Despite its innocent appearance, this lemma and its… (More)

- David Conlon, Jacob Fox, Benny Sudakov
- J. Comb. Theory, Ser. B
- 2012

The Erdős-Hajnal conjecture states that if a graph on n vertices is H-free, that is, it does not contain an induced copy of a given graph H, then it must contain either a clique or an independent set… (More)

- David Conlon, Jacob Fox, Benny Sudakov
- Random Struct. Algorithms
- 2009

We give a short proof that any k-uniform hypergraph H on n vertices with bounded degree ∆ has Ramsey number at most c(∆, k)n, for an appropriate constant c(∆, k). This result was recently proved by… (More)