Geodetic Contraction Games on Trees

  • Yue-Li WangEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10336)


The geodetic contraction game was introduced by Fraenkel and Harary (Int. J. Game Theor. 18:327–338, 1989). They showed that the problem on trees can be solved by using the algorithm for solving the Hackendot game. However, if we use the algorithm for solving the Hackendot game directly, then it will take \(O(n^3)\) time for solving the geodetic contraction game on trees, where n is the number of vertices in a tree. They also posed the following open question: Is there a more efficient strategy to solve the geodetic contraction game on trees? In this paper, we show that the geodetic contraction game on trees can be solved in \(O(n\log n)\) time.


  1. 1.
    Bouton, C.: Nim, a game with a complete mathematical theory. Ann. Math. 3, 35–39 (1902)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Conway, J.H.: On Numbers and Games. CRC Press, London (1976)zbMATHGoogle Scholar
  3. 3.
    Fraenkel, A., Harary, F.: Geodetic contraction games on graphs. Int. J. Game Theory 18, 327–338 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Gale, D., Neymann, A.: Nim-type games. Int. J. Game Theory 11, 17–20 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Úlehla, J.: A complete analysis of Von Neumann’s Hackendot. Int. J. Game Theory 9, 107–113 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Deuber, W., Thomassé, S.: Grundy sets of partial orders. (1996, preprint)

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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Digital Multimedia DesignNational Taipei University of BusinessTaipeiTaiwan

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