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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 ... Most of these methods operate in O(n) ...
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 ...
The nature of a witness value often depends on the type of mathematical calculation being performed. For LEDA's planarity testing function, If the graph is planar, a combinatorial embedding is produced as a witness. If not, a Kuratowski subgraph is returned. These values can then be passed directly to checker functions to confirm their validity.
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 same is true for detecting whether the pattern graph is an induced subgraph of the larger graph, or whether it has a graph homomorphism to the larger graph. [ 48 ] [ 49 ] For the same reason, the problem of testing whether a graph of bounded book thickness obeys a given formula of first order logic is fixed-parameter tractable .
Blossom tree (graph theory) Book (graph theory) Bull graph; Butterfly graph; C. ... Planar straight-line graph; Planarity; Planarity testing; Planarization ...