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PreprintCC BY 4.0arXiv

A short proof of the Erd\H os--Sós Conjecture

  • Oliver Riordan
  • Alex Scott
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Abstract

The Erd\H os--Sós Conjecture was recently proved by GPT-6 Astra, using a very ingenious and surprising argument. In this note, we present a simplified version of this argument in an (arguably) more natural form. We also prove a related conjecture of Addario-Berry, Havet, Linhares Sales, Reed and Thomassé, and give a substantially simplified proof of an analogous result for eulerian digraphs, again proved by GPT-6 Astra, and announced by Mubayi and Verstraete. In addition, we determine the extremal (di)graphs for all three problems.

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Cite

BibTeXRIS
BibTeX
@misc{riordan2026short,
  title = {{A short proof of the Erd\H os--Sós Conjecture}},
  author = {Oliver Riordan and Alex Scott},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.15893},
  eprint = {2609.15893},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15893},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A short proof of the Erd\H os--Sós Conjecture
AU  - Oliver Riordan
AU  - Alex Scott
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.15893
UR  - https://arxiv.org/abs/2609.15893
AB  - The Erd\H os--Sós Conjecture was recently proved by GPT-6 Astra, using a very ingenious and surprising argument. In this note, we present a simplified version of this argument in an (arguably) more natural form. We also prove a related conjecture of Addario-Berry, Havet, Linhares Sales, Reed and Thomassé, and give a substantially simplified proof of an analogous result for eulerian digraphs, again proved by GPT-6 Astra, and announced by Mubayi and Verstraete. In addition, we determine the extremal (di)graphs for all three problems.
ER  -