Jayanthan–Raghavan conjecture on linear type binomial edge ideals

Let $G$ be a graph, and let its binomial edge ideal be the ideal generated by the binomials associated to the edges of $G$. A graph is unicyclic if it has exactly one cycle. Jayanthan–Raghavan's conjecture. If $G$ is a tree or a unicyclic graph, then its binomial edge ideal is of linear type. This conjecture proposes a graph-theoretic characterization of linear type for binomial edge ideals; the supplied source does not provide evidence of a resolution, so its status remains open.