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arXiv · 2606.06202

Exact extremal constructions for the inducibility of blowup graphs

Wanfang Chen·Xizhi Liu
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Abstract

For a finite graph $H$ and a positive integer $h$, the $h$-blowup $H^{(h)}$ of $H$ is the graph obtained by replacing each vertex of $H$ by a set of size $h$ and each edge by a complete bipartite graph between the corresponding sets. We prove that, for every $H$, there exists a constant $h_*(H)$ such that whenever $h\ge h_*(H)$ and $n$ is sufficiently large, every $n$-vertex graph maximizing the number of induced copies of $H^{(h)}$ is a blowup of $H$. This refines the asymptotic result of Hatami, Hirst and Norine and settles the question posed by Bollobás, Egawa, Harris and Jin in 1995.

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Wanfang Chen, Xizhi Liu. 2026-06-04. Exact extremal constructions for the inducibility of blowup graphs. https://arxiv.org/abs/2606.06202

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