7 papers
On the ErdÅs-Rogers function
Robert Morris, Julian Sahasrabudhe, Jacques Verstraëte
We show that the ErdÅs-Rogers function satisfies for every . More precisely, we construct a -free graph o…
A polynomial improvement for the odd cycle-complete Ramsey numbers
Marcelo Campos, Matthew Jenssen, Marcus Michelen +2
We give a polynomial improvement to the cycle-complete Ramsey numbers \[ r(C_{\ell},K_k) \geq k^{1+1/(\ell- 2) + \varepsilon_{\ell} + o(1)}, \] for all fixed odd with $k…
The multicolour size Ramsey number of a path
Csongor Beke, Anqi Li, Julian Sahasrabudhe
In this paper, we determine the -colour size Ramsey number of the path , up to constants. In particular, for every fixed and , we have \[ \wide…
Upper bounds for multicolour Ramsey numbers
Paul Balister, Béla Bollobás, Marcelo Campos +5
The -colour Ramsey number is the minimum such that every -colouring of the edges of the complete graph on vertices contains a monochroma…
Probabilistic combinatorics at exponentially small scales
Julian Sahasrabudhe
In many applications of the probabilistic method, one looks to study phenomena that occur ``with high probability''. More recently however, in an attempt to understand some of the…
An exponential improvement for diagonal Ramsey
Marcelo Campos, Simon Griffiths, Robert Morris +1
The Ramsey number is the minimum such that every red-blue colouring of the edges of the complete graph on vertices contains a monochromatic copy…