Abstract
We have generalized the theory of Shannon's games in [10]. In this paper, we treat a game on a graph with an action of elementary abelian group but our decision of the winner is more general. Our theory can be applied for non-negative integersn andr, to the two games on a graph withn + 1 distinguished terminals whose rules are as follows:
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(1)
the players Short and Cut play alternately to choose an edge,
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(2)
the former contracts it and the later deletes it
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(3)
the former\(\left\{ {_{loses}^{wins} } \right\}\) if and only if he connects the terminals into at mostn − r + 1 ones.
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References
Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Ways. New York: Academic Press 1982
Brualdi, R.A.: Net works and the Shannon switching game. Delta4, 1–23 (1974)
Edmonds, J.: Lehman's switching game and a theorem of Tutte and Nash-Williams. J. Res. Natl. Bur. Stand.69B, 73–77 (1965)
Kano, M.: Generalization of Shannon switching game (private communication)
Lefshetz, S.: Application of Algebraic Topology. New York: Springer-Verlag 1975
Lehman, A.: A solution of the Shannon switching game. SIAM J. Comput.12, 687–725 (1964)
Nash-Williams, C. St. J.A.: Edge-disjoint spanning trees of finite graphs. J. London Math. Soc.36, 445–450 (1961)
Yamasaki, Y.: Theory of division games. Publ. RIMS Kyoto Univ.14, 337–358 (1978)
Yamasaki, Y.: Theory of connexes I, Publ. Res. Inst. Math. Sci.17, 777–812 (1981)
Yamasaki, Y.: Shannon switching games without terminals I (submitted)
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Dedicated to Professor Sin Hitotumatu for his 60'th birthday
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Yamasaki, Y. Shannon switching games without terminals II. Graphs and Combinatorics 5, 275–282 (1989). https://doi.org/10.1007/BF01788679
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DOI: https://doi.org/10.1007/BF01788679