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A simplified proof of the Erd\H{o}s-S-S\'os conjecture on trees in graphs is presented, which is based on its recent resolution by GPT-6 Astra and characterized the extremal examples for Kalai's conjecture.
We present a simplified proof of the Erd\H{o}s-S\'os Conjecture on trees in graphs, which is based on its recent resolution by GPT-6 Astra. At the same time, we also give another proof of the corresponding conjecture for antidirected trees in digraphs, posed by Addario-Berry, Havet, Linhares Sales, Reed, and Thomass\'e...
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