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Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations -
Shakhar Smorodinsky (2010)
Conflict-Free Coloring and its ApplicationsArXiv, abs/1005.3616
- Publisher
- Springer Journals
- Copyright
- Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
- Subject
- Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
- ISSN
- 0933-5846
- eISSN
- 1432-0665
- DOI
- 10.1007/s00153-018-0654-z
- Publisher site
- See Article on Publisher Site
Abstract
Working in subsystems of second order arithmetic, we formulate several representations for hypergraphs. We then prove the equivalence of various vertex coloring theorems to $${\textsf {WKL}}_0$$ WKL 0 , $${\textsf {ACA}}_0$$ ACA 0 , and $${\varPi ^1_1 \text {-}}{\textsf {CA}}_0$$ Π 1 1 - CA 0 .
Journal
Archive for Mathematical Logic – Springer Journals
Published: Nov 29, 2018