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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.
Matching games are games that require players to match similar elements. Participants need to find a match for a word, picture, tile or card. For example, students place 30 word cards; composed of 15 pairs, face down in random order. Each person turns over two cards at a time, with the goal of turning over a matching pair, by using their memory.
A proper vertex coloring of the Petersen graph with 3 colors, the minimum number possible. In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain constraints, such as that no two adjacent elements have the same color.
Rules can be changed here too: it can be agreed before the game starts that matching pairs be any two cards of the same rank, a color-match being unnecessary, or that the match must be both rank and card suit. The game ends when the last pair has been picked up. The winner is the person with the most pairs. There may be a tie for first place.
3-dimensional matchings. (a) Input T. (b)–(c) Solutions. In the mathematical discipline of graph theory, a 3-dimensional matching is a generalization of bipartite matching (also known as 2-dimensional matching) to 3-partite hypergraphs, which consist of hyperedges each of which contains 3 vertices (instead of edges containing 2 vertices in a usual graph).
The second innovation in tile-matching games was the incorporation of their mechanic into other genres. One of the first such games was Puzzle Quest: Challenge of the Warlords released in 2008. While based on a Bejeweled-like tile-matching game, Puzzle Quest added elements of a computer role-playing game atop this.
Matching pennies is a non-cooperative game studied in game theory. It is played between two players, Even and Odd. Each player has a penny and must secretly turn the penny to heads or tails. The players then reveal their choices simultaneously. If the pennies match (both heads or both tails), then Even wins and keeps both pennies.
Tile-matching video games are a type of puzzle video game where the player manipulates tiles in order to make them disappear according to a matching criterion. There are a great number of variations on this theme.