Tournament heroes

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Maria Chudnovsky, Columbia University
Fine Hall 314

The chromatic number of a tournament $T4 is the smallest number of transitive tournaments that partition$V(T)$. Let us say that a tournament$S$is a hero if for every tournament$T$not containing$S$, the chromatic number of$T$is at most a constant$c(S)\$. Recently, in joint work with Eli Berger, Krzysztof Choromanski, Jacob Fox, Martin Loebl, Alex Scott, Paul Seymour and Stephan Thomasse, we proved a theorem that gives a complete description of all heroes. This talk will describe the result, and survey some of the proof ideas.