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Generalized Erdős-Rogers problems for hypergraphs
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DOI：10.1016/j.ejc.2026.104372.png)
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Abstract
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Given r-uniform hypergraphs G and F and an integer n, let fF,G(n) be the maximum m such that every n-vertex G-free r-graph has an F-free induced subgraph on m vertices. We show that fF,G(n) is polynomial in n when G is a subgraph of an iterated blowup of F. As a partial converse, we show that if G is not a subgraph of an Fiterated blowup and is 2-tightly connected, then fF,G(n) is at most polylogarithmic in n. Our bounds generalize previous results of Dudek and Mubayi for the case when F and G are complete. (c) 2026 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
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