{"id":"openai-math/The-strong-thin-tree-conjecture","pdf":"https://github.com/openai/math/blob/main/preprints/The-strong-thin-tree-conjecture-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-strong-thin-tree-conjecture-September-23-2026","tags":["graph-theory","combinatorics","spanning-trees"],"score":0,"title":"The strong thin tree conjecture","domain":"Combinatorics","family":"174","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CO","summary":"We prove that every finite loopless k -edge-connected multigraph on at least two vertices, with k ≥ 1, has a spanning tree meeting each cut in at most $`C/k`$ times the size of the cut, where C is a universal constant. This resolves the strong thin tree conjecture.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":true,"family_title":"Deterministic construction of strong thin spanning trees"}