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Kayles on the Way to the Stars

  • Rudolf Fleischer
  • Gerhard Trippen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3846)

Abstract

We present several new results on the impartial two-person game Kayles. The original version is played on a row of pins (“kayles”). We investigate variants of the game played on graphs. We solve a previously stated open problem in proving that determining the value of a game position needs only polynomial time in a star of bounded degree, and therefore finding the winning move – if one exists – can be done in linear time based on the data calculated before.

Keywords

Polynomial Time Periodic Sequence Single Vertex Simple Path Center Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Ways for Your Mathematical Plays, 2nd edn. A K Peters, Ltd., Wellesley (2001)MATHGoogle Scholar
  2. 2.
    Bodlaender, H.L., Kratsch, D.: Kayles and Nimbers. J. Algorithms 43(1), 106–119 (2002)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Conway, J.H.: On Numbers and Games, 2nd edn. A K Peters, Ltd., Wellesley (2001)MATHGoogle Scholar
  4. 4.
    Fraenkel, A.S.: Recent results and questions in combinatorial game complexities. In: Expanded version of invited lecture at Ninth Australasian Workshop on Combinatorial Algorithms, Perth, Western Australia, July 27–30, pp. 124–146 (1998); Iliopoulos, C. (ed.): Proc. AWOCA 1998, pp. 124–146 (1998)Google Scholar
  5. 5.
    Guy, R.K., Smith, C.A.B.: The G-values of various games. In: Proc. Cambridge Philos. Soc., vol. 52, pp. 514–526 (1956)Google Scholar
  6. 6.
    Kano, M.: Edge-removing games of star type. Discrete Mathematics 151, 113–119 (1996)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Schaefer, T.J.: On the complexity of some two-person perfect-information games. Journal of Computer and System Sciences 16, 185–225 (1978)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Siegel, A.: Combinatorial Game Suite (2003), http://cgsuite.sourcefourge.net/

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Rudolf Fleischer
    • 1
  • Gerhard Trippen
    • 2
  1. 1.Shanghai Key Laboratory of Intelligent Information Processing, Department of Computer Science and EngineeringFudan UniversityShanghaiChina
  2. 2.Department of Computer ScienceThe Hong Kong University of Science and TechnologyHong Kong

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