Ramsey, expanders, and Borel chromatic numbers
Jan Greb\'ik, Zolt\'an Vidny\'anszky
TL;DR
This paper constructs bounded degree acyclic Borel graphs with high Borel chromatic numbers by leveraging Ramsey theory and expander graph limits, advancing understanding of graph coloring complexities in descriptive set theory.
Contribution
It introduces a novel construction of Borel graphs with large chromatic numbers using Ramsey-theoretic and expander sequence techniques.
Findings
Constructed bounded degree acyclic Borel graphs with large Borel chromatic number
Utilized Ramsey theory and expander sequences in the construction
Demonstrated the existence of complex Borel graphs with high chromatic properties
Abstract
We construct bounded degree acyclic Borel graphs with large Borel chromatic number using a graph arising from Ramsey theory and limits of expander sequences.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Limits and Structures in Graph Theory · Computability, Logic, AI Algorithms