On tangencies among planar curves with an application to coloring L-shapes

no code implementations • 4 Mar 2021 • Eyal Ackerman, Balázs Keszegh, Dömötör Pálvölgyi

We prove that there are $O(n)$ tangencies among any set of $n$ red and blue planar curves in which every pair of curves intersects at most once and no two curves of the same color intersect.

Combinatorics

Saturation problems in the Ramsey theory of graphs, posets and point sets

no code implementations • 13 Apr 2020 • Gábor Damásdi, Balázs Keszegh, David Malec, Casey Tompkins, Zhiyu Wang, Oscar Zamora

We prove a saturation version of the Erd\H{o}s-Szekeres theorem about monotone subsequences and saturation versions of some Ramsey-type theorems on graphs and Dilworth-type theorems on posets.

Combinatorics

Line Percolation in Finite Projective Planes

no code implementations • 1 Aug 2016 • Dániel Gerbner, Balázs Keszegh, Gábor Mészáros, Balázs Patkós, Máté Vizer

We study combinatorial parameters of a recently introduced bootstrap percolation problem in finite projective planes.

Combinatorics