Erdős 146 degeneracy-based extremal-number conjecture
Follow the latest progress by email.
How well can an extremal edge-count exponent be predicted from the degree and degeneracy structure of a forbidden graph? Erdős Problem 146 asks this for the specified connected bipartite two-degenerate class, with a proposed n^(3/2) scale.
Why it matters and what counts as progress
Why it matters: A larger extremal exponent would show that two-degeneracy and the stated degree conditions do not force the proposed density scale.
What counts as progress: Construct a graph in the stated degree class with extremal number at least c n^(3/2+ε), or prove a valid restricted exponent theorem.
How the problem developed
- 1984 · Conjecture [1]
Paul Erdős and Miklós Simonovits The problem collection attributes the bound ex(n,H) = O(n^(2−1/r)) for bipartite r-degenerate graphs to Erdős and Simonovits.
- 2003 · Partial result [1]
Noga Alon, Michael Krivelevich and Benny Sudakov Proved a weaker general exponent and the conjectured exponent under an additional maximum-degree condition on one bipartition side.
OpenAI internal model Reported a fixed connected bipartite 2-degenerate graph H with ex(n,H) at least c·n^(3/2+ε), disproving the universal conjecture at r = 2.
AI contribution
Ten Advances in Mathematics and Theoretical Computer Science
A connected bipartite two-degenerate graph H meeting the stated degree conditions has extremal number at least c n^(3/2+ε) for some c,ε>0. This contradicts the proposed exponent for that class.
Sources
Website timeline
Publication dates and editorial changes.