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arXiv · 1804.08991

Domination game and minimal edge cuts

Sandi Klavžar·Douglas F. Rall
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Abstract

In this paper a relationship is established between the domination game and minimal edge cuts. It is proved that the game domination number of a connected graph can be bounded above in terms of the size of minimal edge cuts. In particular, if $C$ a minimum edge cut of a connected graph $G$, then $\gamma_g(G) \le \gamma_g(G\setminus C) + 2\kappa'(G)$. Double-Staller graphs are introduced in order to show that this upper bound can be attained for graphs with a bridge. The obtained results are used to extend the family of known traceable graphs whose game domination numbers are at most one-half their order. Along the way two technical lemmas, which seem to be generally applicable for the study of the domination game, are proved.

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Sandi Klavžar, Douglas F. Rall. 2018-04-24. Domination game and minimal edge cuts. https://arxiv.org/abs/1804.08991

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