We study criteria attesting that a given graph can not be embedded in the plane so that neighboring vertices are at unit distance apart and the straight line edges do not cross.
@article{arxiv.1401.4375,
title = {Fast regocnition of planar non unit distance graphs},
author = {Sascha Kurz},
journal= {arXiv preprint arXiv:1401.4375},
year = {2014}
}