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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.
The source code has also been released; the game is still being sold on CD, but the open source version contains the full game content. Boppin' 1994 2005 [29] Puzzle Amiga, DOS Apogee Software: Castle Infinity: 1996 2000 MMOG: Windows: Starwave: Castle of the Winds: 1989 1998 [30] Role-playing video game: Windows 3.x: Epic MegaGames: Caves of ...
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
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A 2-spot game of Sprouts. The game ends when the first player is unable to draw a connecting line between the only two free points, marked in green. The game is played by two players, [2] starting with a few spots drawn on a sheet of paper. Players take turns, where each turn consists of drawing a line between two spots (or from a spot to ...
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).
Proof without words that a hypercube graph is non-planar using Kuratowski's or Wagner's theorems and finding either K 5 (top) or K 3,3 (bottom) subgraphs. If is a graph that contains a subgraph that is a subdivision of or ,, then is known as a Kuratowski subgraph of . [1]
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.