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In graph theory, the planarity testing problem is the algorithmic problem of testing whether a given graph is a planar graph (that is, ...
In graph theory, a branch of mathematics, the left-right planarity test or de Fraysseix–Rosenstiehl planarity criterion [1] is a characterization of planar graphs based on the properties of the depth-first search trees, published by de Fraysseix and Rosenstiehl (1982, 1985) [2] [3] and used by them with Patrice Ossona de Mendez to develop a linear time planarity testing algorithm.
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
In graph theory, Mac Lane's planarity criterion is a characterisation of planar graphs in terms of their cycle spaces, named after Saunders Mac Lane who published it in 1937. It states that a finite undirected graph is planar if and only if the cycle space of the graph (taken modulo 2) has a cycle basis in which each edge of the graph ...
A Kuratowski subgraph of a nonplanar graph can be found in linear time, as measured by the size of the input graph. [2] This allows the correctness of a planarity testing algorithm to be verified for nonplanar inputs, as it is straightforward to test whether a given subgraph is or is not a Kuratowski subgraph. [3]
The Hopcroft–Tarjan planarity testing algorithm was the first linear-time algorithm for planarity testing. [11] Tarjan has also developed important data structures such as the Fibonacci heap (a heap data structure consisting of a forest of trees), and the splay tree (a self-adjusting binary search tree; co-invented by Tarjan and Daniel Sleator).
Blossom tree (graph theory) Book (graph theory) Bull graph; Butterfly graph; C. ... Planar straight-line graph; Planarity; Planarity testing; Planarization ...
Matching (graph theory) MaxDDBS; Maximal independent set; Maximum agreement subtree problem; Maximum common edge subgraph; Maximum common induced subgraph; Maximum cut; Maximum flow problem; Maximum weight matching; Metric k-center; Minimum k-cut; Mixed Chinese postman problem; Multi-trials technique