16 citations · 33 across the 22 of their papers we have counts for
33 papers
On the Erdős-Rogers function
Robert Morris, Julian Sahasrabudhe, Jacques Verstraëte
We show that the Erdős-Rogers function satisfies for every . More precisely, we construct a -free graph on…
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…
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…
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…
A new lower bound for the Ramsey numbers
Marcelo Campos, Matthew Jenssen, Marcus Michelen +1
We prove a new lower bound for the off-diagonal Ramsey numbers, \[ R(3,k) \geq \bigg( \frac{1}{3}+ o(1) \bigg) \frac{k^2}{\log k }\, , \] thereby narrowing the gap between the uppe…
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…