{"id":"openai-math/A-proof-of-Seymours-second-neighborhood-conjecture","pdf":"https://github.com/openai/math/blob/main/preprints/A-proof-of-Seymours-second-neighborhood-conjecture-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-proof-of-Seymours-second-neighborhood-conjecture-September-23-2026","tags":["graph-theory","digraphs","combinatorics"],"score":0,"title":"A proof of Seymour’s second-neighborhood conjecture","domain":"Combinatorics","family":"173","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CO","summary":"We prove that every nonempty finite oriented graph has a vertex with at least as many vertices at directed distance two as at directed distance one. This resolves Seymour's second neighborhood conjecture positively.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":true,"family_title":"Seymour’s second-neighborhood conjecture"}