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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.
Download as PDF; Printable version; In other projects ... Book (graph theory) Bull graph; Butterfly graph; C. Cactus graph; ... Planar straight-line graph; Planarity ...
Minor testing (checking whether an input graph contains an input graph as a minor); the same holds with topological minors; Steiner tree, or Minimum spanning tree for a subset of the vertices of a graph. [2] (The minimum spanning tree for an entire graph is solvable in polynomial time.) Modularity maximization [5]
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 subdivision of a graph is a graph formed by subdividing its edges into paths of one or more edges. Kuratowski's theorem states that a finite graph G {\displaystyle G} is planar if it is not possible to subdivide the edges of K 5 {\displaystyle K_{5}} or K 3 , 3 {\displaystyle K_{3,3}} , and then possibly add additional edges and vertices, to ...
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.
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. [1] [2] Such a drawing is called a plane graph, or a planar embedding of the graph.