We construct, for each countable ordinal ξ, a closed graph with Borel chromatic number 2 and Baire class ξ chromatic number ℵ₀.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm152-11-2015,
author = {Dominique Lecomte and Miroslav Zelen\'y},
title = {Borel chromatic number of closed graphs},
journal = {Fundamenta Mathematicae},
volume = {233},
year = {2016},
pages = {163-169},
zbl = {06602787},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm152-11-2015}
}
Dominique Lecomte; Miroslav Zelený. Borel chromatic number of closed graphs. Fundamenta Mathematicae, Tome 233 (2016) pp. 163-169. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm152-11-2015/