LIPIcs.STACS.2010.2483.pdf
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Is Ramsey's Theorem omega-automatic?
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27th International Symposium on Theoretical Aspects of Computer Science (STACS 2010)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Theoretical Aspects of Computer Science (STACS) - License:
Creative Commons Attribution-NoDerivs 3.0 Unported license
- Publication Date: 2010-03-09
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Dietrich Kuske. Is Ramsey's Theorem omega-automatic?. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 537-548, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)
https://doi.org/10.4230/LIPIcs.STACS.2010.2483
Abstract
We study the existence of infinite cliques in $\omega$-automatic (hyper-)graphs. It turns out that the situation is much nicer than in general uncountable graphs, but not as nice as for automatic graphs. More specifically, we show that every uncountable $\omega$-automatic graph contains an uncountable co-context-free clique or anticlique, but not necessarily a context-free (let alone regular) clique or anticlique. We also show that uncountable $\omega$-automatic ternary hypergraphs need not have uncountable cliques or anticliques at all.
Subject Classification
Keywords
- Logic in computer science
- automata
- Ramsey theory
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