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Embedding nearly spanning trees

Part of: Graph theory

Published online by Cambridge University Press:  11 August 2025

Bruce Reed  and
Maya Stein Open the ORCID record for Maya Stein [Opens in a new window]
Bruce Reed
Affiliation:
Institute of Mathematics, Academica Sinica, Taipei, Taiwan
Maya Stein*
Affiliation:
Department of Mathematical Engineering and Center for Mathematical Modeling (CNRS IRL2807), University of Chile, Santiago, Chile
*
Corresponding author: Maya Stein; Email: mstein@dim.uchile.cl
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Abstract

The Erdős-Sós Conjecture states that every graph with average degree exceeding $k-1$ contains every tree with $k$ edges as a subgraph. We prove that there are $\delta \gt 0$ and $k_0\in \mathbb N$ such that the conjecture holds for every tree $T$ with $k \ge k_0$ edges and every graph $G$ with $|V(G)| \le (1+\delta )|V(T)|$.

Keywords

TreesGraphsDegreespanningaverage degree

MSC classification

Primary: 05C35: Extremal problems 05C05: Trees 05C07: Vertex degrees

Information

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 34 , Issue 6 , November 2025 , pp. 927 - 931
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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Footnotes

*

Dedicated to the memory of Vera T. Sós.

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