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The Fraysseix–Rosenstiehl planarity criterion can be used directly as part of algorithms for planarity testing, while Kuratowski's and Wagner's theorems have indirect applications: if an algorithm can find a copy of K 5 or K 3,3 within a given graph, it can be sure that the input graph is not planar and return without additional computation.
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.
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 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).
The original graph will be represented as an immersion minor of its planarization. In incremental planarization, the planarization process is split into two stages. First, a large planar subgraph is found within the given graph. Then, the remaining edges that are not already part of this subgraph are added back one at a time, and routed through ...
Book (graph theory) Bull graph; Butterfly graph; C. ... Left-right planarity test; Friendship graph; Frucht graph; G. Goldner–Harary graph; Golomb graph; Good ...
In graph theory, the Weisfeiler Leman graph isomorphism test is a heuristic test for the existence of an isomorphism between two graphs G and H. [1] It is a generalization of the color refinement algorithm and has been first described by Weisfeiler and Leman in 1968. [ 2 ]
In computational geometry and geometric graph theory, a planar straight-line graph (or straight-line plane graph, or plane straight-line graph), in short PSLG, is an embedding of a planar graph in the plane such that its edges are mapped into straight-line segments. [1] Fáry's theorem (1948) states that every planar graph has this kind of ...