google-deepmind / google-deepmind/formal-conjectures
Erdős Problem 603
Open
ams-03: Mathematical logic and foundations
ams-05: Combinatorics
erdos-problems
new conjecture
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Description
### What is the conjecture
https://www.erdosproblems.com/603
Let $(A_i)$ be a family of countable sets such that $\lvert A_i\cap A_j\rvert \neq 2$ for all $i\neq j$. Is there some $C$ such that $\cup A_i$ can always be coloured with at most $C$ colours so that no $A_i$ is monochromatic?
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
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Assessment
This issue has not been assessed yet.