eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2010-03-09
537
548
10.4230/LIPIcs.STACS.2010.2483
article
Is Ramsey's Theorem omega-automatic?
Kuske, Dietrich
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol005-stacs2010/LIPIcs.STACS.2010.2483/LIPIcs.STACS.2010.2483.pdf
Logic in computer science
automata
Ramsey theory