graph invariant at most two or three, the linklessly embeddable graphs are the graphs that have Colin de Verdière invariant at most four. See also Combinatorial map a combinatorial object that can encode plane graphs Planarization, a planar graph formed from a drawing with crossings by replacing each crossing point by a new vertex Thickness (graph theory), the smallest number of planar graphs into which the edges of a given graph may be partitioned Planarity, a puzzle computer game in which the objective is to embed a planar graph onto a plane Sprouts (game), a pencil-and-paper game where a planar graph subject to certain constraints is constructed as part of the game play Three utilities problem, a popular puzzle Notes References . . . . . Special Issue on Graph Drawing. . External links Edge Addition Planarity Algorithm Source Code, version 1.0 — Free C source code for reference implementation of Boyer–Myrvold planarity algorithm, which provides both a combinatorial planar embedder and Kuratowski subgraph isolator. An open source project with free licensing provides the Edge Addition Planarity Algorithms, current version. Public Implementation of a Graph Algorithm Library and Editor — GPL graph algorithm library including planarity testing, planarity embedder and Kuratowski subgraph exhibition in linear time. Boost Graph Library tools for planar graphs, including linear time planarity testing, embedding, Kuratowski subgraph isolation, and straight-line drawing. 3 Utilities Puzzle and Planar Graphs NetLogo Planarity model — NetLogo version of John Tantalo's game Graph families Intersection classes of graphs