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The sharp terminal leave in random triangle removal
Starting from the complete graph on n vertices, repeatedly delete a uniformly chosen remaining triangle. The terminal edge count is asymptotic to , with mean-square convergence after normalization by n. This proves the triangle case of the Joos–Kühn sharp-constant conjecture.
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The sharp terminal leave in random triangle removal
Sep 25, 2026·The-Sharp-Terminal-Leave-in-Random-Triangle-Removal-September-25-2026.pdf
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, converges in L to . 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.