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/