Molnár-Sáska Zoltán: A proof of the Erdős-Sands-Sauer-Woodrow conjecture

A classical result of Sands, Sauer, and Woodrow states that every 2-edge-colored tournament contains a single vertex that monochromatically reaches all other vertices. The Erdős-Sands-Sauer-Woodrow conjecture (ESSW) generalised this for more colors and was proved by Bousquet, Lochet, and Thomassé 35 years later
in 2017. I will present this proof, mention some related variations and briefly discuss a recent application to colorings of geometric hypergraphs in the work of Damásdi and Pálvölgyi.

Based on the following papers:
https://arxiv.org/abs/1703.08123
https://arxiv.org/abs/2112.01820