google-deepmind / google-deepmind/formal-conjectures
Erdős Problem 719
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Description
### What is the conjecture
https://www.erdosproblems.com/719
Let $\mathrm{ex}\_r(n; K_{r+1}^r)$ be the maximum number of $r$-edges that can be placed on $n$ vertices without forming a $K_{r+1}^r$ (the $r$-uniform complete graph on $r+1$ vertices).
Is every $r$-hypergraph $G$ on $n$ vertices the union of at most $\mathrm{ex}\_{r}(n;K_{r+1}^r)$ many copies of $K_r^r$ and $K_{r+1}^r$, no two of which share a $K_r^r$?
Status: open
### 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
Research direction
No file, test, or entry point is named in the issue. Start by reading the linked Erdős Problems 719 statement and the repository's existing formalized conjectures; done means adding a corresponding formal statement to the collection with the project's expected validation passing.
Written by the indexing model from the issue text.
Assessment
- Domain
- devtools
- Issue type
- Feature
- Difficulty
- 5/5
- Estimated time
- Over a week
- Activity status
- Stale
- Clarity
- Needs clarification
- Newbie friendliness
- 30/100