Peter Keevash

activity

20242026

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7 papers · 1 filter

math.CO2026

A very robust Ramsey theorem for matchings

Peter Keevash, Peleg Michaeli

Our main result is a robust generalisation of the Cockayne-Lorimer theorem on the multicolour Ramsey number of matchings. It is moreover a generalisation of the transference genera…

math.CO2025

A generalised Ramsey--Turán problem for matchings

Peter Keevash, Peleg Michaeli

We prove a generalised Ramsey--Turán theorem for matchings, which (a) simultaneously generalises the Cockayne--Lorimer Theorem (Ramsey for matchings) and the Erdős--Gallai Theorem…

math.CO2025

On subsets of lattice cubes avoiding affine and spherical degeneracies

Anubhab Ghosal, Ritesh Goenka, Peter Keevash

For integers $1 < k < d - 1$ and $r \geq k + 2$ , we establish new lower bounds on the maximum number of points in $[n]^{d}$ such that no $r$ lie in a $k$ -dimensional affine (or linear) su…

math.CO2025

Cyclic subsets in regular Dirac graphs

Nemanja Draganić, Peter Keevash, Alp Müyesser

In 1996, in his last paper, Erdős asked the following question that he formulated together with Faudree: is there a positive $c$ such that any $(n + 1)$ -regular graph $G$ on $2 n$ ver…

math.CO2025

Pósa rotation through a random permutation

Nemanja Draganić, Peter Keevash

What minimum degree of a graph $G$ on $n$ vertices guarantees that the union of $G$ and a random $2$ -factor (or permutation) is with high probability Hamiltonian? Girão and Espuny…

math.CO2024

A short proof of the existence of designs

Peter Keevash

We give a new proof of the existence of designs, which is much shorter and gives better bounds.