Erdős 621

### What is the conjecture

https://www.erdosproblems.com/621

Let $G$ be a graph on $n$ vertices, $\alpha_1(G)$ be the maximum number of edges that contain at most one edge from every triangle, and $\tau_1(G)$ be the minimum number of edges that contain at least one edge from every triangle.

Is it true that
$$\alpha_1(G)+\tau_1(G) \leq \frac{n^2}{4}?$$

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