The sharp terminal leave in random triangle removal
OpenAI research collection · 1 manuscript · Source checked 2026-10-19
OpenAI's result summary
Starting from the complete graph on n vertices, repeatedly delete a uniformly chosen remaining triangle. The terminal edge count is asymptotic to n^{3/2}/(2\sqrt2), with mean-square convergence after normalization by n^(3/2). This proves the triangle case of the Joos–Kühn sharp-constant conjecture.
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The sharp terminal leave in random triangle removal
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,…
Full source abstract
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.
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