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Jeux combinatoires sur les graphes

Abstract : Everyone has ever played a combinatorial game, such as chess or checkers. The interest of mathematicians about this subject is often related to the search of a winning strategy for one of both players. From the game of Nim to chess, the complexity of this search is very variable. In this manuscript, we firstly give a short view of the main stages of the topic, who really started in the beginning of the XXth century. Besides, we emphasize the correlation between combinatorial games and number theory, error-correcting codes, or graph theory. We then investigate some variations of « classical » combinatorial games : Wythoff's game and Dots and Boxes. We detail the strategy and « good » game positions for the first and the second player. We then consider a solitaire variation of a recent two-player game : Clobber. It is a one-player game, where stones are placed on the vertices of a given graph. A move consisting in removing a stone (under some conditions), the goal is to minimize the number of remaining stones at the end. We give structural and algorithmic results about this game played on grids, trees or hypercubes.
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Contributor : Eric Duchene <>
Submitted on : Wednesday, September 20, 2006 - 5:31:22 PM
Last modification on : Friday, November 6, 2020 - 3:58:25 AM
Long-term archiving on: : Thursday, September 20, 2012 - 10:51:21 AM


  • HAL Id : tel-00097047, version 1



Eric Duchene. Jeux combinatoires sur les graphes. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2006. Français. ⟨tel-00097047⟩



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