Related papers: The Maker-Maker domination game in forests
In the Maker-Breaker domination game, Dominator and Staller play on a graph $G$ by taking turns in which each player selects a not yet played vertex of $G$. Dominator's goal is to select all the vertices in a dominating set, while Staller…
The domination game is played on a graph $G$ by two players, named Dominator and Staller. They alternatively select vertices of $G$ such that each chosen vertex enlarges the set of vertices dominated before the move on it. Dominator's goal…
In this paper we consider positional games where the winning sets are tree universal graphs. Specifically, we show that in the unbiased Maker-Breaker game on the complete graph $K_n$, Maker has a strategy to occupy a graph which contains…
In 2010, Bre\v{s}ar, Klav\v{z}ar and Rall introduced the optimization variant of the graph domination game and the game domination number, which was proved PSPACE-hard by Bre\v{s}ar et al. in 2016. In 2024, Leo Versteegen obtained the…
We analyze the domination game, where two players, Dominator and Staller, construct together a dominating set M in a given graph, by alternately selecting vertices into M. Each move must increase the size of the dominated set. The players…
The domination game on a graph $G$ (introduced by B. Bre\v{s}ar, S. Klav\v{z}ar, D.F. Rall \cite{BKR2010}) consists of two players, Dominator and Staller, who take turns choosing a vertex from $G$ such that whenever a vertex is chosen by…
The Maker-Maker convention of positional games is played on a hypergraph whose edges are interpreted as winning sets. Two players take turns picking a previously unpicked vertex, aiming at being first to pick all the vertices of some edge.…
In the Maker-Breaker positional game, Maker and Breaker take turns picking vertices of a hypergraph $H$, and Maker wins if and only if she possesses all the vertices of some edge of $H$. Deciding the outcome (i.e. which player has a winning…
The Maker-Breaker domination game is played on a graph $G$ by two players, called Dominator and Staller, who alternately choose a vertex that has not been played so far. Dominator wins the game if his moves form a dominating set. Staller…
In a Maker-Breaker game on a graph $G$, Breaker and Maker alternately claim edges of $G$. Maker wins if, after all edges have been claimed, the graph induced by his edges has some desired property. We consider four Maker-Breaker games…
The Maker-Breaker domination game is played on a graph $G$ by Dominator and Staller who alternate turns selecting an unplayed vertex of $G$. The goal of Dominator is that the vertices he selected during the game form a dominating set while…
The domination game is played on a graph G. Vertices are chosen, one at a time, by two players Dominator and Staller. Each chosen vertex must enlarge the set of vertices of G dominated to that point in the game. Both players use an optimal…
We study biased {\em orientation games}, in which the board is the complete graph $K_n$, and Maker and Breaker take turns in directing previously undirected edges of $K_n$. At the end of the game, the obtained graph is a tournament. Maker…
In this paper, we continue the study of the total domination game in graphs introduced in [Graphs Combin. 31(5) (2015), 1453--1462], where the players Dominator and Staller alternately select vertices of $G$. Each vertex chosen must…
The classical Maker-Breaker positional game is played on a board which is a hypergraph $\mathcal{H}$, with two players, Maker and Breaker, alternately claiming vertices of $\mathcal{H}$ until all the vertices are claimed. When the game…
We introduce and analyze the Walker-Breaker game, a variant of Maker-Breaker games where Maker is constrained to choose edges of a walk or path in a given graph G, with the goal of visiting as many vertices of the underlying graph as…
We study the Maker-Breaker domination game played by Dominator and Staller on the vertex set of a given graph. Dominator wins when the vertices he has claimed form a dominating set of the graph. Staller wins if she makes it impossible for…
The domination game is an optimization game played by two players, Dominator and Staller, who alternately select vertices in a graph $G$. A vertex is said to be dominated if it has been selected or is adjacent to a selected vertex. Each…
We investigate a game played between two players, Maker and Breaker, on a countably infinite complete graph where the vertices are the rational numbers. The players alternately claim unclaimed edges. It is Maker's goal to have after…
In the Maker-Breaker resolving game, two players named Resolver and Spoiler alternately select unplayed vertices of a given graph $G$. The aim of Resolver is to select all the vertices of some resolving set of $G$, while Spoiler aims to…