English

Small unit-distance graphs in the plane

Combinatorics 2019-05-27 v3

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.

Keywords

Cite

@article{arxiv.1905.07829,
  title  = {Small unit-distance graphs in the plane},
  author = {Aidan Globus and Hans Parshall},
  journal= {arXiv preprint arXiv:1905.07829},
  year   = {2019}
}

Comments

(v3) fixed F(9,15,21) and Lemma 19

R2 v1 2026-06-23T09:12:21.553Z