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Planarity is a 2005 puzzle computer game by John Tantalo, based on a concept by Mary Radcliffe at Western Michigan University. [1] The name comes from the concept of planar graphs in graph theory; these are graphs that can be embedded in the Euclidean plane so that no edges intersect.
In mathematics, Whitney's planarity criterion is a matroid-theoretic characterization of planar graphs, named after Hassler Whitney. [1] It states that a graph G is planar if and only if its graphic matroid is also cographic (that is, it is the dual matroid of another graphic matroid).
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; Three utilities problem, a popular puzzle
Planarity [ edit ] A pointed pseudotriangulation is a planar straight-line drawing of a graph, with the properties that the outer face is convex, that every bounded face is a pseudotriangle , a polygon with only three convex vertices, and that the edges incident to every vertex span an angle of less than 180 degrees.
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).
Play free online Canasta. Meld or go out early. Play four player Canasta with a friend or with the computer.
A planar graph cannot contain K 3,3 as a minor; an outerplanar graph cannot contain K 3,2 as a minor (These are not sufficient conditions for planarity and outerplanarity, but necessary). Conversely, every nonplanar graph contains either K 3,3 or the complete graph K 5 as a minor; this is Wagner's theorem. [9]
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