Maximum Number of Almost Similar Triangles in the Plane

no code implementations • 25 Jan 2021 • József Balogh, Felix Christian Clemen, Bernard Lidický

A triangle $T'$ is $\varepsilon$-similar to another triangle $T$ if their angles pairwise differ by at most $\varepsilon$.

Combinatorics 52C45, 05D05, 05C65

On tripartite common graphs

no code implementations • 3 Dec 2020 • Andrzej Grzesik, Joonkyung Lee, Bernard Lidický, Jan Volec

The conjectures by Erdos and by Burr and Rosta were disproved by Thomason and by Sidorenko, respectively, in the late 1980s.

Combinatorics

Maximizing five-cycles in $K_r$-free graphs

no code implementations • 6 Jul 2020 • Bernard Lidický, Kyle Murphy

The Erd\H{o}s Pentagon problem asks to find an $n$-vertex triangle-free graph that is maximizing the number of $5$-cycles.

Combinatorics