Salvetti–Serventi connected homology graph conjecture for real arrangements

Let ${\mathcal A}$ be a real affine line arrangement, and let $\Gamma({\mathcal A})$ be the graph whose vertices are the lines $H\in{\mathcal A}$, with an edge $(H,H')$ exactly when $H\cap H'$ is a point of multiplicity two. An arrangement is a-monodromic when no nontrivial monodromy eigenvalues occur. Salvetti–Serventi's conjecture. If $\Gamma({\mathcal A})$ is connected, then ${\mathcal A}$ is a-monodromic. This conjecture concerns when the combinatorics of an arrangement force trivial monodromy on the Milnor fiber; its status is open in the supplied source.