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Descriptive Chromatic Numbers of Locally Finite and Everywhere Two Ended Graphs
release_5nrakc3yave45jlmhlpjwccg5i
by
Felix Weilacher
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2020
Abstract
We construct Borel graphs which settle several questions in descriptive graph
combinatorics. These include "Can the Baire measurable chromatic number of a
locally finite Borel graph exceed the usual chromatic number by more than one?"
and "Can marked groups with isomorphic Cayley graphs have Borel chromatic
numbers for their shift graphs which differ by more than one?" We also provide
a new bound for Borel chromatic numbers of graphs whose connected components
all have two ends.
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arXiv
2004.02316v1
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