Hameed's conjecture on semi-transitivity of Mycielski graphs

Let $G$ be a graph, and let $\mu(G)$ denote its Mycielski graph. A graph is semi-transitive if it admits an acyclic orientation with no shortcut. Hameed's conjecture. For every graph $G$, the graph $\mu(G)$ is semi-transitive if and only if $G$ is a bipartite graph. Hameed proved this equivalence when $G$ is a comparability graph, while the assertion for arbitrary graphs remains open.