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
no code implementations • 11 Jun 2020 • Péter Ágoston, Dömötör Pálvölgyi
We prove that the number of unit distances among $n$ planar points is at most $1. 94\cdot n^{4/3}$, improving on the previous best bound of $8n^{4/3}$.
Combinatorics Discrete Mathematics
no code implementations • 29 Nov 2018 • Dömötör Pálvölgyi, Gábor Tardos
In this note we disprove a conjecture of Kuzmin and Warmuth claiming that every family whose VC-dimension is at most d admits an unlabeled compression scheme to a sample of size at most d. We also study the unlabeled compression schemes of the joins of some families and conjecture that these give a larger gap between the VC-dimension and the size of the smallest unlabeled compression scheme for them.
