Title
Chromatic numbers of stable graphs
Abstract
Given a graph (G,E), its chromatic number is the smallest cardinal kappa of a legal coloring of the vertices. Taylor conjectured that if the chromatic number of G is > aleph0 then for every cardinal kappa, G has an elementary extension with chromatic number > kappa (this wasn’t his precise conjecture, but it’s close enough). Although this turned out to be (consistently) false in general, we are able to recover variants of this conjecture (and even the strong Taylor conjecture, which is false in general) for stable graphs.
This is joint work with Yatir Halevi and Saharon Shelah.
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