For K4-free graphs, the graphic arrangement group embeds in a product of free groups, so it is residually free, torsion-free, and acts properly on a CAT(0) cube complex.
Cohen, Monodromy of fiber-type arrangements and orbit configuration spaces , Fo- rum Math
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On graphic arrangement groups
For K4-free graphs, the graphic arrangement group embeds in a product of free groups, so it is residually free, torsion-free, and acts properly on a CAT(0) cube complex.