Erdős Problem 993

### What is the conjecture

https://www.erdosproblems.com/993

The independent set sequence of any tree or forest is unimodal.

In other words, if $i_k(G)$ counts the number of independent sets of vertices of size $k$ in a graph $G$, and $T$ is any tree or forest, then for some $m\geq 0$
$$i_{0}(T)\leq i_{1}(T)\leq\cdots\leq i_{m}(T)\geq i_{m+1}(T)\geq i_{m+2}(T)\geq\cdots.$$

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