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Conference Papers Year : 2010

Is Ramsey's theorem omega-automatic?


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.
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inria-00457041 , version 1 (16-02-2010)


  • HAL Id : inria-00457041 , version 1


Dietrich Kuske. Is Ramsey's theorem omega-automatic?. 27th International Symposium on Theoretical Aspects of Computer Science - STACS 2010, Inria Nancy Grand Est & Loria, Mar 2010, Nancy, France. pp.537-548. ⟨inria-00457041⟩
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