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Graph Theory pp 135-148 | Cite as

My Favorite Domination Game Conjectures

  • Michael A. HenningEmail author
Chapter
Part of the Problem Books in Mathematics book series (PBM)

Abstract

The domination game belongs to the growing family of competitive optimization graph games, and describes a process in which two players, Dominator and Staller, with conflicting goals collaboratively produce a dominating set in an underlying host graph. The players take turns choosing a vertex from the graph, where each vertex chosen must dominate at least one vertex not dominated by the set of vertices previously chosen. The game ends when there are no more moves available. The players’ goals are completely antithetical: while Dominator wants to minimize the size of a dominating set, Staller wants to maximize it. In this chapter, we discuss some of the conjectures on domination-type game parameters.

Notes

Acknowledgements

Research supported in part by the South African National Research Foundation and the University of Johannesburg.

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.University of JohannesburgDepartment of Pure and Applied MathematicsAuckland ParkSouth Africa

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