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Graph pebbling is a mathematical game played on a graph with zero or more pebbles on each of its vertices. 'Game play' is composed of a series of pebbling moves. A pebbling move on a graph consists of choosing a vertex with at least two pebbles, removing two pebbles from it, and adding one to an adjacent vertex (the second removed pebble is discarded from play). π(G), the pebbling number of a ...
The results for misère play are now conjectured to follow a pattern of length six with some exceptional values: the first player wins in misère Sprouts when the remainder (mod 6) is zero, four, or five, except that the first player wins the one-spot game and loses the four-spot game. The table below shows the pattern, with the two irregular ...
This will also apply to any super-graph of K 6. For another proof that there must eventually be a triangle of either color, see the Theorem on friends and strangers. Computer search has verified that the second player can win Sim with perfect play, but finding a perfect strategy that humans can easily memorize is an open problem. [1]
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The game requires players to slow down before bends in the track, and requires some foresight and planning for successful play. The game is popular as an educational tool teaching vectors . The game is also known under names such as Vector Formula , Vector Rally , Vector Race , Graph Racers , PolyRace , Paper and pencil racing , or the Graph ...
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In graph theory, a tournament is a directed graph with exactly one edge between each two vertices, in one of the two possible directions.Equivalently, a tournament is an orientation of an undirected complete graph.
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