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How Long Can One Bluff in the Domination Game?

Boštan BrešarPaul DorbecSandi KlavžarGašpar Košmrlj — 2017

Discussiones Mathematicae Graph Theory

The domination game is played on an arbitrary graph G by two players, Dominator and Staller. The game is called Game 1 when Dominator starts it, and Game 2 otherwise. In this paper bluff graphs are introduced as the graphs in which every vertex is an optimal start vertex in Game 1 as well as in Game 2. It is proved that every minus graph (a graph in which Game 2 finishes faster than Game 1) is a bluff graph. A non-trivial infinite family of minus (and hence bluff) graphs is established. minus graphs...

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