9 papers · 1 filter
No--in-line problem for
Anubhab Ghosal, Ritesh Goenka, Alexandr Grebennikov +3
What is the maximum number of points one can place in an grid such that every Euclidean line contains at most points? For , this is the notorious no-three-i…
On the largest sum-free subset of the lattice cube
Peter Keevash, Jeck Lim
We determine the limiting density of the largest sum-free subset of the lattice cube for all , thus resolving the natural conjecture that it is constructed…
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…
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 ErdÅs--Gallai Theore…
On subsets of lattice cubes avoiding affine and spherical degeneracies
Anubhab Ghosal, Ritesh Goenka, Peter Keevash
For integers and , we establish new lower bounds on the maximum number of points in such that no lie in a -dimensional affine (or linear) su…
Cyclic subsets in regular Dirac graphs
Nemanja DraganiÄ, Peter Keevash, Alp Müyesser
In 1996, in his last paper, ErdÅs asked the following question that he formulated together with Faudree: is there a positive such that any -regular graph on ve…