Computational problems in graph theory | Planar graphs

Planarity testing

In graph theory, the planarity testing problem is the algorithmic problem of testing whether a given graph is a planar graph (that is, whether it can be drawn in the plane without edge intersections). This is a well-studied problem in computer science for which many practical algorithms have emerged, many taking advantage of novel data structures. Most of these methods operate in O(n) time (linear time), where n is the number of edges (or vertices) in the graph, which is asymptotically optimal. Rather than just being a single Boolean value, the output of a planarity testing algorithm may be a planar graph embedding, if the graph is planar, or an obstacle to planarity such as a Kuratowski subgraph if it is not. (Wikipedia).

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Related pages

Planar graph | Mac Lane's planarity criterion | Glossary of graph theory | Big O notation | Graphic matroid | Depth-first search | Colin de Verdière graph invariant | Cycle space | Wagner's theorem | Graph theory | Complete bipartite graph | Induced subgraph | Vertex (graph theory) | Complete graph | Kuratowski's theorem | PQ tree | Graph isomorphism | Schnyder's theorem | Spectral graph theory | Utility graph | Whitney's planarity criterion | Shimon Even | Order dimension | Graph embedding | Algorithm