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.
Borel chromatic numbers: finite vs infinite
08.06.2017 15:00 - 16:30
Organiser:
KGRC
Location:
SR 101, 2. St., Währinger Str. 25