# BOREL CHROMATIC NUMBERS

@article{Kechris1999BORELCN, title={BOREL CHROMATIC NUMBERS}, author={Alexander S. Kechris and Slawomir Solecki and Stevo Todorcevic}, journal={Advances in Mathematics}, year={1999}, volume={141}, pages={1-44} }

We study in this paper graph coloring problems in the context of descriptive set theory. We consider graphs G=(X, R), where the vertex set X is a standard Borel space (i.e., a complete separable metrizable space equipped with its σ-algebra of Borel sets), and the edge relation R ⊆ X^2 is
"definable", i.e., Borel, analytic, co-analytic, etc.
A Borel n-coloring of such a graph, where 1⩽ n ⩽ N_0 , is a Borel map c: X → Y with card(Y)=n, such
that xRy⇒c(x) ≠ {c( y). If such a Borel coloring…

## 186 Citations

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