Finding Increasingly Large Extremal Graphs with AlphaZero and Tabu Search

no code implementations • 6 Nov 2023 • Abbas Mehrabian, Ankit Anand, Hyunjik Kim, Nicolas Sonnerat, Matej Balog, Gheorghe Comanici, Tudor Berariu, Andrew Lee, Anian Ruoss, Anna Bulanova, Daniel Toyama, Sam Blackwell, Bernardino Romera Paredes, Petar Veličković, Laurent Orseau, Joonkyung Lee, Anurag Murty Naredla, Doina Precup, Adam Zsolt Wagner

This work studies a central extremal graph theory problem inspired by a 1975 conjecture of Erd\H{o}s, which aims to find graphs with a given size (number of nodes) that maximize the number of edges without having 3- or 4-cycles.

Decision Making Graph Generation

On graph norms for complex-valued functions

no code implementations • 28 Jan 2021 • Joonkyung Lee, Alexander Sidorenko

One may also extend this to complex-valued functions, once $H$ is paired with a $2$-edge-colouring $\alpha$ to assign conjugates.

Combinatorics Functional Analysis 05C22, 05C60, 15A60

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