Minimal triangle density in graphs (AlphaEvolve problem 46)
Minimal triangle density in graphs (AlphaEvolve problem 46). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.
Editorial MSC2020 classification. Original article codes and source evidence are recorded in the literature directory.
Problem statement
For , let denote the largest quantity such that any graph on vertices and edges will have at least triangles. What is ?
Lean 4
No Lean statement or proof is attached yet. Have a formalization? Share its source to add it to this problem.
Background
Repository result category: matched optimal — AlphaEvolve matched the known or conjectured optimum. See Section 6.27 in "Mathematical Exploration and Discovery at Scale " paper: arXiv:2511.02864. Experiment notebook.
Progress & source assessment
The repository page records no bounds for this problem.
- [1]Georgiev, Bogdan; Gómez-Serrano, Javier; Tao, Terence; Wagner, Adam Zsolt. Repository of problems accompanying “Mathematical exploration and discovery at scale” (arXiv:2511.02864), github.com/google-deepmind/alphaevolve_repository_of_problems (commit 8f44745, 11 July 2026). — Minimal triangle density in graphs (AlphaEvolve problem 46) linkApache-2.0 (repository license); problem pages reproduced with attribution.
Recorded progress
Add yours →Nothing recorded yet. A pointer to a paper the entry is missing counts.
Machine attempts
0 recordedAttempts run against the statement below and are recorded in full, including the failures. The point is to stop the next model — and the next person — from re-walking a road that is already known to end. Each attempt costs 25 credits.
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Discussion
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