Joint work with Chris Lambie-Hanson.

**Abstract.** We prove that reflection of the coloring number of graphs is consistent with non-reflection of the chromatic number. Moreover, it is proved that incompactness for the chromatic number of graphs (with arbitrarily large gaps) is compatible with each of the following compactness principles: Rado’s conjecture, Fodor-type reflection, $\Delta$-reflection, Stationary-sets reflection, Martin’s Maximum, and a generalized Chang’s conjecture.

This is accomplished by showing that, under GCH-type assumptions, instances of incompactness for the chromatic number can be derived from square-like principles that are compatible with large amounts of compactness.

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Update Feb/2017: Added a new section, entitled “Realizing all closed intervals”.

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Submitted to Combinatorica, December 2016.

Accepted, June 2017.

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