{"id":"openai-math/The-Sharp-Terminal-Leave-in-Random-Triangle-Removal","pdf":"https://github.com/openai/math/blob/main/preprints/The-Sharp-Terminal-Leave-in-Random-Triangle-Removal-September-25-2026/The-Sharp-Terminal-Leave-in-Random-Triangle-Removal-September-25-2026.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-Sharp-Terminal-Leave-in-Random-Triangle-Removal-September-25-2026","tags":["random-graphs","combinatorics","probability"],"score":0,"title":"The sharp terminal leave in random triangle removal","domain":"Combinatorics","family":"188","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CO","summary":"Starting from the complete graph on n vertices, repeatedly remove the three edges of a uniformly chosen remaining triangle. We prove that the number of edges left at termination, divided by n 3/2 , converges in L 2 to $`1/(2\\sqrt2)`$. This proves the triangle case of the sharp-constant conjecture of Joos and Kühn. In particular, the same limit holds in probability and for the normalized expectation.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":false,"family_title":"The sharp terminal leave in random triangle removal"}