google-deepmind / google-deepmind/formal-conjectures

Erdős Problem 1021

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ams-05: Combinatorics erdos-problems new conjecture
Dominant language
Lean
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Description

### What is the conjecture

https://www.erdosproblems.com/1021

Is it true that, for every $k\geq 3$, there is a constant $c_k>0$ such that
$$\mathrm{ex}(n,G_k) \ll n^{3/2-c_k},$$
where $G_k$ is the bipartite graph between $\\{y_1,\ldots,y_k\\}$ and $\\{z_1,\ldots,z_{\binom{k}{2}}\\}$, with each $z_j$ joined to a unique pair of $y_i$?

Status: solved

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else

Contributor guide

Open the contributing guide

Research direction

No source files, tests, or entry points are mentioned. Start by reviewing the repository's conventions for formalized conjectures and the linked Erdős problem, then determine the required formal statement and validation approach; done means the conjecture is added in the project's expected form and its checks pass.

Written by the indexing model from the issue text.

Assessment

Domain
tooling
Issue type
Feature
Difficulty
5/5
Estimated time
Over a week
Activity status
Stale
Clarity
Needs clarification
Newbie friendliness
25/100

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