google-deepmind / google-deepmind/formal-conjectures

Erdős Problem 719

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ams-05: Combinatorics erdos-problems new conjecture
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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

Open the contributing 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

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