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The Shannon switching game can be seen as a special case of a Maker-Breaker game, in which the winning patterns for the Maker are connecting paths. A weakly-related connection game Hex is played on a grid of hexagons, and has 6-connectivity. Generalized Hex is played on a graph, just like the Shannon game, but instead of coloring the edges, in ...
For a general players game, in which each player has possible strategies, the size of a normal form representation would be (). The size of the graphical representation for this game is O ( m d ) {\displaystyle O(m^{d})} where d {\displaystyle d} is the maximal node degree in the graph.
Hex is a finite, 2-player perfect information game, and an abstract strategy game that belongs to the general category of connection games. [1] It can be classified as a Maker-Breaker game, [1]: 122 a particular type of positional game. Since the game can never end in a draw, [1]: 99 Hex is also a determined game.
The Battle for Wesnoth, a hex grid based computer game. A hex map, hex board, or hex grid is a game board design commonly used in simulation games of all scales, including wargames, role-playing games, and strategy games in both board games and video games. A hex map is subdivided into a hexagonal tiling, small regular hexagons of identical size.
The icosian game itself has been the topic of multiple works in recreational mathematics by well-known authors on the subject including Édouard Lucas, [2] Wilhelm Ahrens, [18] and Martin Gardner. [12] Puzzles like Hamilton's icosian game, based on finding Hamiltonian cycles in planar graphs, continue to be sold as smartphone apps. [19]
In the planarity game, the player is presented with a circular layout of a planar graph, with all the vertices placed on a single circle and with many crossings. The goal for the player is to eliminate all of the crossings and construct a straight-line embedding of the graph by moving the vertices one by one into better positions.
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The graph coloring game is a mathematical game related to graph theory. Coloring game problems arose as game-theoretic versions of well-known graph coloring problems. In a coloring game, two players use a given set of colors to construct a coloring of a graph, following specific rules depending on the game we consider.