Dense Minors from the Crux

Xia Wang; Donglei Yang

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arXiv · 2610.39957

Dense Minors from the Crux

Xia Wang·Donglei Yang

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Abstract

Let $G$ be a graph with average degree $d>0$ and $C_α(G)$ be the minimum order of a subgraph whose average degree is at least $αd$ for any fixed $0<α<1$. Then $G$ has a minor of average degree $Ω(\sqrt{d\,C_α(G)})$, which is asymptotically tight up to a constant factor. This reveals a unified mechanism underlying previous results on dense minors in locally sparse graphs.

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Xia Wang, Donglei Yang. 2026-10-29. Dense Minors from the Crux. https://arxiv.org/abs/2610.39957

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