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Shannon Switching Game and Directed Variants

Claudio, A. P.; Fonseca, S. ; Sequeira, Luís; Silva, I. P.

Dynamics, Games and Science. CIM Series in Mathematical Sciences, 1 (2015), 187-199

Shannon’s switching game is a combinatorial game invented by C. Shannon circa 1955 as a simple model for breakdown repair of the connectivity of a network. The game was completely solved by A. Lehman, shortly after, in what is considered the first application of matroid theory. In the middle 1980s Y. O. Hamidoune and M. Las Vergnas introduced and solved directed versions of the game for graphs considering their generalization to oriented matroids. We do a brief review of the main results and conjectures of the directed case.