拉姆齐定理是ω-自动的吗？

摘要：

研究了Ω-自动（超）图中无限团的存在性。事实证明，这种情况比一般的不可数图要好得多，但不如自动图好。更具体地说，我们证明了每一个不可数的欧米茄自动图包含一个不可数的co-context-free集团或anticlique，但不一定是一个上下文无关（更不用说定期）集团或anticlique。我们还证明了不可数的Ω-自动三元超图根本不需要有不可数的团或反团。

英文摘要：

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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