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.
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References
Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Ways for Your Mathematical Plays, 2nd edn. A K Peters, Ltd., Wellesley (2001)
Bodlaender, H.L., Kratsch, D.: Kayles and Nimbers. J. Algorithms 43(1), 106–119 (2002)
Conway, J.H.: On Numbers and Games, 2nd edn. A K Peters, Ltd., Wellesley (2001)
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)
Guy, R.K., Smith, C.A.B.: The G-values of various games. In: Proc. Cambridge Philos. Soc., vol. 52, pp. 514–526 (1956)
Kano, M.: Edge-removing games of star type. Discrete Mathematics 151, 113–119 (1996)
Schaefer, T.J.: On the complexity of some two-person perfect-information games. Journal of Computer and System Sciences 16, 185–225 (1978)
Siegel, A.: Combinatorial Game Suite (2003), http://cgsuite.sourcefourge.net/
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© 2006 Springer-Verlag Berlin Heidelberg
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Fleischer, R., Trippen, G. (2006). Kayles on the Way to the Stars. In: van den Herik, H.J., Björnsson, Y., Netanyahu, N.S. (eds) Computers and Games. CG 2004. Lecture Notes in Computer Science, vol 3846. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11674399_16
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DOI: https://doi.org/10.1007/11674399_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-32488-1
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