On the freeness of Boroczky line arrangements

In the present note, we focus on the freeness and some combinatorial properties of line arrangements in the projective plane having only double and triple points. The main result shows that for this class of line arrangements the freeness property is combinatorially determined. As a corollary, we show that Boroczky line arrangements in the sense of Furedi and Palasti (Proc Am Math Soc 92(4):561-566, 1984), except exactly three cases, are not free.