Domination game and minimal edge cuts.

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 γ g (G) ≤ γ g (G ∖ C) + 2 κ ′ (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. [ABSTRACT FROM AUTHOR]