Logo image
The Erdős–Sós Conjecture: A visual exposition of the proof discovered by GPT-6 Astra
Preprint

The Erdős–Sós Conjecture: A visual exposition of the proof discovered by GPT-6 Astra

Jay Cummings
09/25/2026

Abstract

Mathematics - General Mathematics
The Erdős–Sós theorem states that every graph of average degree greater thant-2contains every tree ontvertices. A short counting proof was discovered by GPT-6 Astra in 2026. We give a visual, reader-centered exposition of that argument whose presentation differs substantially from the original. We recast the counting objects as early neighbors in a reveal-and-stop procedure, organize the induction through explicit partitions and reversible swaps, and develop the proof through worked examples with consistent drawings. We also give direct and probabilistic conclusions, compare this formulation with other recent expositions, and record the classical consequenceR(T;q)≤ q(t-2)+2for multicolor Ramsey numbers of trees.

Metrics

1 Record Views

Details

Title
The Erdős–Sós Conjecture: A visual exposition of the proof discovered by GPT-6 Astra
Creators
Jay Cummings - California State University, Sacramento
Academic Unit
Mathematics
Identifiers
99258354011301671; https://doi.org/10.48550/arxiv.2609.32011
Language
English
Logo image