David Conlon

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math.CO2024

When are off-diagonal hypergraph Ramsey numbers polynomial?

David Conlon, Jacob Fox, Benjamin Gunby +5

A natural open problem in Ramsey theory is to determine those $3$ -graphs $H$ for which the off-diagonal Ramsey number $r (H, K_{n}^{(3)})$ grows polynomially with $n$ . We make substan…

math.CO2024

Non-spherical sets versus lines in Euclidean Ramsey theory

David Conlon, Jakob Führer

We show that for every non-spherical set $X$ in $E^{d}$ , there exists a natural number $m$ and a red/blue-colouring of $E^{n}$ for every $n$ such that there is no red…

math.CO2024

On off-diagonal hypergraph Ramsey numbers

David Conlon, Jacob Fox, Benjamin Gunby +4

A fundamental problem in Ramsey theory is to determine the growth rate in terms of $n$ of the Ramsey number $r (H, K_{n}^{(3)})$ of a fixed $3$ -uniform hypergraph $H$ versus the compl…

math.CO2024

A question of Erdős and Graham on Egyptian fractions

David Conlon, Jacob Fox, Xiaoyu He +4

Answering a question of Erdős and Graham, we show that for each fixed positive rational number $x$ the number of ways to write $x$ as a sum of reciprocals of distinct positive inte…