On May 13, 2025, Seokbeom Kim (김석범) from KAIST and the IBS Discrete Mathematics Group gave a talk on the structure of tournaments without a fixed 5-vertex tournament and its applications to the dichromatic number at the Discrete Math Seminar. The title of his talk was “The structure of △(1, 2, 2)-free tournaments“.
Given a tournament , a tournament is -free if it has no subtournament isomorphic to . Until now, there have been only a small number of tournaments such that the complete structure of -free tournaments is known.
Let be a tournament obtained from the cyclic triangle by substituting two-vertex tournaments for two of its vertices. In this talk, we present a structure theorem for -free tournaments, which was previously unknown. As an application, we provide tight bounds for the chromatic number as well as the size of the largest transitive subtournament for such tournaments.
This talk is based on joint work with Taite LaGrange, Mathieu Rundström, Arpan Sadhukhan, and Sophie Spirkl.
The IBS discrete mathematics group welcomes Seokbeom Kim (김석범), a new graduate student at the IBS discrete mathematics group since August 2022. He is currently a graduate student at the department of mathematical sciences, KAIST.
