Fast regocnition of planar non unit distance graphs

TL;DR

This paper investigates criteria to determine when a graph cannot be embedded in the plane with edges of unit length without crossings, aiding in understanding planar non-unit distance graphs.

Contribution

It introduces new criteria for recognizing non-embeddability of graphs in the plane with unit distances and crossing-free edges.

Findings

New criteria for non-embeddability established

Enhanced understanding of planar non-unit distance graphs

Potential algorithms for graph recognition developed

Abstract

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.