integral drawing

An integral embedding of a graph, not to be confused with an integral graph, is a graph drawn such that vertices are distinct points and all graph edges have integer lengths. Every graph possesses an integral embedding (Müller 1953, Harborth and Möller 1994). It is conjectured that every planar graph has a plane integral embedding. A unit-distance graph is a graph that not only possesses an integral embedding, but an embedding in which all edges have the same length (which can be taken as 1 without loss of generality). Unit-distance embeddings are therefore minimal integral embeddings since they have the smallest possible (1) largest edge length.

graph embedding | planar embedding | planar graph | unit-distance embedding | unit-distance graph