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arXiv · 2603.09521

Induced subdivisions of $K_{d+1}$ in graphs of high girth

António Girão·Zach Hunter
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Abstract

In this paper, we show that for all $k\geq 10^8$, every graph with minimum degree $k$ and girth at least $10^8$ contains an induced subdivision of a $K_{k+1}$. This answers a problem asked by Kühn and Osthus (originally attributed to Shi).

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António Girão, Zach Hunter. 2026-03-10. Induced subdivisions of $K_{d+1}$ in graphs of high girth. https://arxiv.org/abs/2603.09521

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