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 with game domination number equal to 3 are characterized. Double bluff graphs are also introduced and it is proved that Kneser graphs K(n, 2), n ≥ 6, are double bluff. The domination game is also studied on generalized Petersen graphs and on Hamming graphs. Several generalized Petersen graphs that are bluff graphs but not vertex-transitive are found. It is proved that Hamming graphs are not double bluff.
@article{bwmeta1.element.doi-10_7151_dmgt_1899,
author = {Bo\v stan Bre\v sar and Paul Dorbec and Sandi Klav\v zar and Ga\v spar Ko\v smrlj},
title = {How Long Can One Bluff in the Domination Game?},
journal = {Discussiones Mathematicae Graph Theory},
volume = {37},
year = {2017},
pages = {337-352},
zbl = {06705132},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1899}
}
Boštan Brešar; Paul Dorbec; Sandi Klavžar; Gašpar Košmrlj. How Long Can One Bluff in the Domination Game?. Discussiones Mathematicae Graph Theory, Tome 37 (2017) pp. 337-352. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1899/