Combinatorics in one-based and related structures

Artem Chernikov; Sergei Starchenko

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arXiv · 2606.08740

Combinatorics in one-based and related structures

Artem Chernikov·Sergei Starchenko

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Abstract

We consider some extremal combinatorial questions for bipartite graphs definable in stable one-based (and related) structures. We show that they satisfy both strong Erd\H{o}s-Hajnal property and linear Zarankiewicz. We also show that the same is true for both collapsed and uncollapsed Hrushovski's ``ab initio'' constructions, and discuss some connections to Zilber's trichotomy principle. For strong Erd\H{o}s-Hajnal, we show that in fact it holds in a more general class of $1$-semi-equational theories.

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BibTeX RIS

Artem Chernikov, Sergei Starchenko. 2026-06-07. Combinatorics in one-based and related structures. https://arxiv.org/abs/2606.08740

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