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math.CO2023
Permutation Tutte polynomial
Csongor Beke, Gergely Kál Csáji, Péter Csikvári +1
The classical Tutte polynomial is a two-variate polynomial 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 of any matroid 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 vertices is at most , which is sharp by the balanced blow-up of a pentagon. This…