Small unit-distance graphs in the plane
arXiv:1905.07829
Abstract
We prove that a graph on up to 9 vertices is a unit-distance graph if and only if it does not contain one of 74 so-called minimal forbidden graphs. This extends the work of Chilakamarri and Mahoney (1995), who provide a similar classification for unit-distance graphs on up to 7 vertices.
(v3) fixed F(9,15,21) and Lemma 19