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arXiv · 2412.19912

Blowing up Dirac's theorem

Richard Lang·Nicolás Sanhueza-Matamala
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Abstract

We show that every graph $G$ on $n$ vertices with $δ(G) \geq (1/2+\varepsilon)n$ is spanned by a complete blow-up of a cycle with clusters of nearly uniform size $Ω(\log n)$. The proof is based on a recently introduced approach for finding vertex-spanning substructures via blow-up covers.

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Richard Lang, Nicolás Sanhueza-Matamala. 2025-12-15. Blowing up Dirac's theorem. https://arxiv.org/abs/2412.19912

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