منابع مشابه
1 9 N ov 2 01 4 The Disjoint Domination Game ∗
We introduce and study a Maker-Breaker type game in which the issue is to create or avoid two disjoint dominating sets in graphs without isolated vertices. We prove that the maker has a winning strategy on all connected graphs if the game is started by the breaker. This implies the same in the (2 : 1) biased game also in the maker-start game. It remains open to characterize the maker-win graphs...
متن کاملDomination Game
The domination game played on a graph G consists of two players, Dominator and Staller who alternate taking turns choosing a vertex from G such that whenever a vertex is chosen by either player, at least one additional vertex is dominated. Dominator wishes to dominate the graph in as few steps as possible and Staller wishes to delay the process as much as possible. The game domination number γg...
متن کاملOn the Computational Complexity of the Domination Game
The domination game is played on an arbitrary graph $G$ by two players, Dominator and Staller. It is known that verifying whether the game domination number of a graph is bounded by a given integer $k$ is PSPACE-complete. On the other hand, it is showed in this paper that the problem can be solved for a graph $G$ in $mathcal O(Delta(G)cdot |V(G)|^k)$ time. In the special case when $k=3$ and the...
متن کاملPaired-Domination Game Played in Graphs
In this paper, we continue the study of the domination game in graphs introduced by Bre{v{s}}ar, Klav{v{z}}ar, and Rall. We study the paired-domination version of the domination game which adds a matching dimension to the game. This game is played on a graph $G$ by two players, named Dominator and Pairer. They alternately take turns choosing vertices of $G$ such that each vertex chosen by Domin...
متن کاملDisjoint and unfolding domination in graphs
We consider the problem of finding k disjoint dominating sets with a minimum size of their union, in a given network. We show that this problem can be solved in polynomial time for interval graphs and odd-sun-free graphs. We also relate this question to the so called k-fold domination in graphs. 1 Problem definition and motivation We consider finite undirected graphs without loops or multiple e...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2016
ISSN: 0012-365X
DOI: 10.1016/j.disc.2015.04.028