Geodesic
Two dichotomy theorems on colourability of non-analytic graphs
Fundamenta Mathematicae, Tome 154 (1997) no. 2, pp. 183-201.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We prove:  Theorem 1. Let κ be an uncountable cardinal. Every κ-Suslin graph G on reals satisfies one of the following two requirements: (I) G admits a κ-Borel colouring by ordinals below κ; (II) there exists a continuous homomorphism (in some cases an embedding) of a certain locally countable Borel graph $G_0$ into G.  Theorem 2. In the Solovay model, every OD graph G on reals satisfies one of the following two requirements: (I) G admits an OD colouring by countable ordinals; (II) as above.
DOI : 10.4064/fm-154-2-183-201

Vladimir Kanovei 1

1 
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Vladimir  Kanovei. Two dichotomy theorems on colourability of non-analytic graphs. Fundamenta Mathematicae, Tome 154 (1997) no. 2, pp. 183-201. doi : 10.4064/fm-154-2-183-201. http://geodesic.mathdoc.fr/articles/10.4064/fm-154-2-183-201/

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