Csongor Beke

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math.CO2025

The multicolour size Ramsey number of a path

Csongor Beke, Anqi Li, Julian Sahasrabudhe

In this paper, we determine the $r$ -colour size Ramsey number of the path $P_{k}$ , up to constants. In particular, for every fixed $r \geq 2$ and $k \geq 100 lo g r$ , we have \[ \wide…

math.CO2023

Permutation Tutte polynomial

Csongor Beke, Gergely Kál Csáji, Péter Csikvári +1

The classical Tutte polynomial is a two-variate polynomial $T_{G} (x, y)$ associated to graphs or more generally, matroids. In this paper, we introduce a polynomial $\widetilde{T}_H(x,…

math.CO2023

The Merino--Welsh conjecture is false for matroids

Csongor Beke, Gergely Kál Csáji, Péter Csikvári +1

The matroidal version of the Merino--Welsh conjecture states that the Tutte polynomial $T_{M} (x, y)$ of any matroid $M$ without loops and coloops satisfies that $$\max(T_M(2,0),T_M(0,…

math.CO2023

On the generalized Turán problem for odd cycles

Csongor Beke, Oliver Janzer

In 1984, Erdős conjectured that the number of pentagons in any triangle-free graph on $n$ vertices is at most $(n /5)^{5}$ , which is sharp by the balanced blow-up of a pentagon. This…