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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 uncountablegraphs, but not as nice as for automatic graphs.More specifically, we show that every uncountable omega-automatic graphcontains an uncountable co-context-free clique or anticlique, but notnecessarily a context-free let alone regular clique or anticlique. We alsoshow that uncountable omega-automatic ternary hypergraphs need not haveuncountable cliques or anticliques at all.



Author: Dietrich Kuske

Source: https://arxiv.org/



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