Abstract
Shannon switching game has been analyzed by Lehman [3] in matroid theory. Kano [2] has studied games with many terminals where Short intends to connect at least two of them. This result is included in [6] and [7], where the games are described on graphs with group action. These results will be generalized in this paper which deals with games on a finite set with two matroid structures.
Our new theory can be applied to the game where Short's purpose is to connect all the given pairs of terminals and to the game where Short's purpose is to connect at least one of given two pairs of terminals. On the other hand, the game is not reversible (see [9]) if Short's purpose is to connect at least one of given three pairs of terminals.
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Yamasaki, Y. Shannon switching games without terminals III. Graphs and Combinatorics 8, 291–297 (1992). https://doi.org/10.1007/BF02349966
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DOI: https://doi.org/10.1007/BF02349966