On unavoidable induced subgraphs in large prime graphs

M. Malliaris; C. Terry

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arXiv · 1511.02544

On unavoidable induced subgraphs in large prime graphs

M. Malliaris·C. Terry

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Abstract

Chudnovsky, Kim, Oum, and Seymour recently established that any prime graph contains one of a short list of induced prime subgraphs [1]. In the present paper we reprove their theorem using many of the same ideas, but with the key model-theoretic ingredient of first determining the so-called amount of stability of the graph. This approach changes the applicable Ramsey theorem, improves the bounds and offers a different structural perspective on the graphs in question. Complementing this, we give an infinitary proof which implies the finite result.

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M. Malliaris, C. Terry. 2015-11-09. On unavoidable induced subgraphs in large prime graphs. https://arxiv.org/abs/1511.02544

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