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We construct Borel graphs which settle several questions in descriptive graphcombinatorics. These include "Can the Baire measurable chromatic number of alocally finite Borel graph exceed the usual chromatic number by more than one?"and "Can marked groups with isomorphic Cayley graphs have Borel chromaticnumbers for their shift graphs which differ by more than one?" We also providea new bound for Borel chromatic numbers of graphs whose connected componentsall have two ends.

Descriptive Chromatic Numbers of Locally Finite and Everywhere Two Ended Graphs