In topological graph theory, a mathematical discipline, a **linkless embedding** of an undirected graph is an embedding of the graph into Euclidean space in such a way that no two cycles of the graph have nonzero linking number. A **flat embedding** is an embedding with the property that every cycle is the boundary of a topological disk that is not crossed by any other feature of the graph. A **linklessly embeddable graph** is a graph that has a linkless or flat embedding; these graphs form a three-dimensional analogue of the planar graphs.

Flat embeddings are automatically linkless, but not vice versa. The complete graph *K*_{6}, the Petersen graph, and the other five graphs in the Petersen family do not have linkless embeddings. The linklessly embeddable graphs are closed under graph minors and Y-Δ transforms, have the Petersen family graphs as their forbidden minors, and include the planar graphs and apex graphs. They may be recognized, and a flat embedding may be constructed for them, in linear time.

Read more about Linkless Embedding: Definitions, Examples and Counterexamples, Characterization and Recognition, Related Families of Graphs, History