2017 seminar talk: Borel chromatic numbers: finite vs infinite

Talk held by Zoltán Vidnyánszky (York University, Toronto, Canada) at the KGRC seminar on 2017-06-08.

Abstract

One of the most interesting results of Borel graph combinatorics is the $G_0$ dichotomy, i. e., the fact that a Borel graph has uncountable Borel chromatic number if and only if it contains a Borel homomorphic image of a graph called $G_0$. It was conjectured that an analogous statement could be true for graphs with infinite Borel chromatic number. Using descriptive set theoretic methods we answer this question and a couple of similar questions negatively, showing that one cannot hope for the existence of a Borel graph whose embeddability would characterize Borel (or even closed) graphs with infinite Borel chromatic number. We will also discuss a positive result and its relation to Hedetniemi's conjecture.

Time and Place

Tea at 3:30pm in the KGRC meeting room

Talk at 4:00pm in the KGRC lecture room

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Kurt Gödel Research Center for Mathematical Logic. Währinger Straße 25, 1090 Wien, Austria. Phone +43-1-4277-50501. Last updated: 2010-12-16, 04:37.