Mohr et al.'s low-sum spanning forest conjecture

Let $K_n$ be a complete graph of order $n$, and let $c:E(K_n)\to \{-1,1\}$ be a zero-sum labeling satisfying

$$c(E(K_n))=\sum_{e\in E(K_n)}c(e)=0.$$

Let $F$ be a spanning forest of $K_n$ with maximum degree $\Delta$. Mohr et al.'s conjecture. There is an isomorphic copy $F'$ of $F$ in $K_n$ such that

$$|c(E(F'))|\leq \frac{1}{2}\Delta-\frac{1}{2}.$$

This would improve the previously known bound $|c(E(F'))|\leq \Delta+1$ and concerns the existence of low-sum copies of spanning forests in zero-sum edge-labeled complete graphs. The supplied source does not establish whether the conjecture is resolved.