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arXiv · 2311.01488

A note on universal graphs for spanning trees

Ervin Győri·Binlong Li·Nika Salia·Casey Tompkins
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Abstract

Chung and Graham considered the problem of minimizing the number of edges in an $n$-vertex graph containing all $n$-vertex trees as a subgraph. They showed that such a graph has at least $\frac{1}{2}n \log{n}$ edges. In this note, we improve this lower estimate to $n \log{n}$.

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Ervin Győri, Binlong Li, Nika Salia, Casey Tompkins. 2023-11-06. A note on universal graphs for spanning trees. https://arxiv.org/abs/2311.01488

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