Erdős Problem 761

### What is the conjecture

https://www.erdosproblems.com/761

The cochromatic number of $G$, denoted by $\zeta(G)$, is the minimum number of colours needed to colour the vertices of $G$ such that each colour class induces either a complete graph or empty graph. The dichromatic number of $G$, denoted by $\delta(G)$, is the minimum number $k$ of colours required such that, in any orientation of the edges of $G$, there is a $k$-colouring of the vertices of $G$ such that there are no monochromatic oriented cycles.

Must a graph with large chromatic number have large dichromatic number? Must a graph with large cochromatic number contain a graph with large dichromatic number?

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

Start by reading the conjecture at https://www.erdosproblems.com/761 and the issue description to determine the precise formal statement needed. No repository file, test, or entry point is named, so the appropriate location and validation workflow still need to be investigated. Done means adding a formalization of the conjecture to the collection.

Written by the indexing model from the issue text.