Paper draft claims the Erdős–Simonovits degeneracy conjecture fails for all r ≥ 2
ctjlewis · x · 2026-08-04
A reply points to a draft proof, and the attached paper shows a formal result on the Erdős–Simonovits degeneracy conjecture.
- The paper claims the conjecture is false for all r ≥ 2.
- It presents a layered graph construction and proves a connected bipartite graph Hr with degeneracy exactly r.
- The abstract states that for sufficiently large n, ex(n; Hr) ≥ c n^(2-1/r+1/(28r^2)).
- For r = 3, the exponent improves to 5/3 + 1/160.
- The paper also analyzes the construction’s thresholds, the Gibbs-weight phase transition, and why the method’s ceiling is 1/(8r^2).
The screenshots show the structure of the proof: forbidden graph construction, density thresholds, entropy bounds, and the positivity of the feasible window.
Related event: AI-Assisted Proof Refutes Classic Erdős Degeneracy Conjecture(2 posts)→
More from Research
- UMD's PAIR framework bridges perception and action in VLA models via bridge tokens — Kaixi Feng · 2026-10-16
- CI-MSE offline metric hits -0.87 Spearman correlation with real robot task success vs weak raw MSE — chris_j_paxton · 2026-10-16
- Colossal Biosciences uses AI to decode genetic switches behind the extinct dodo — castrotech · 2026-10-16
- Colossal Biosciences uses AI to identify gene switches in dodo de-extinction push — castrotech · 2026-10-16
- Cheng Lou open-sources Handwired: hand-written weights turn code into training-free neural nets — dotey · 2026-10-16
- Digital-first GLP-1 program delivers 16.1 kg average weight loss across 8,000+ women — EricTopol · 2026-10-16