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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2010.2483
URN: urn:nbn:de:0030-drops-24838
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Kuske, Dietrich

Is Ramsey's Theorem omega-automatic?

1001.KuskeDietrich.2483.pdf (0.3 MB)


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.

BibTeX - Entry

  author =	{Dietrich Kuske},
  title =	{{Is Ramsey's Theorem omega-automaticl}},
  booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{537--548},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-16-3},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{5},
  editor =	{Jean-Yves Marion and Thomas Schwentick},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-24838},
  doi =		{10.4230/LIPIcs.STACS.2010.2483},
  annote =	{Keywords: Logic in computer science, automata, Ramsey theory}

Keywords: Logic in computer science, automata, Ramsey theory
Collection: 27th International Symposium on Theoretical Aspects of Computer Science
Issue Date: 2010
Date of publication: 09.03.2010

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