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We introduce the Maker-Breaker domination game, a two player game on a graph. At his turn, the first player, Dominator, select a vertex in order to dominate the graph while the other player, Staller, forbids a vertex to Dominator in order…

Discrete Mathematics · Computer Science 2018-09-19 Eric Duchêne , Valentin Gledel , Aline Parreau , Gabriel Renault

Maker-Breaker total domination game in graphs is introduced as a natural counterpart to the Maker-Breaker domination game recently studied by Duch\^ene, Gledel, Parreau, and Renault. Both games are instances of the combinatorial…

Combinatorics · Mathematics 2019-02-04 Valentin Gledel , Michael A. Henning , Vesna Iršič , Sandi Klavžar

The Maker-Breaker domination game is a positional game played on a graph by two players called Dominator and Staller. The players alternately select a vertex of the graph that has not yet been chosen. Dominator wins if at some point the…

Combinatorics · Mathematics 2024-06-24 Guillaume Bagan , Eric Duchêne , Valentin Gledel , Tuomo Lehtilä , Aline Parreau

We study Maker--Breaker total domination game played by two players, Dominator and Staller, on the connected cubic graphs. Staller (playing the role of Maker) wins if she manages to claim an open neighbourhood of a vertex. Dominator wins…

Combinatorics · Mathematics 2023-06-22 Jovana Forcan , Mirjana Mikalački

Let $(X, \mathcal{F})$ be a hypergraph. The Maker-Breaker game on $(X, \mathcal{F})$ is a combinatorial game between two players, Maker and Breaker. Beginning with Maker, the players take turns claiming vertices from $X$ that have not yet…

Discrete Mathematics · Computer Science 2025-02-28 Finn Orson Koepke

The Maker-Breaker domination game is played on a graph $G$ by two players, called Dominator and Staller. They alternately select an unplayed vertex in $G$. Dominator wins the game if he forms a dominating set while Staller wins the game if…

Combinatorics · Mathematics 2024-08-20 Pakanun Dokyeesun

We consider a biased version of Maker-Breaker domination games, which were recently introduced by Gledel, Ir{\v{s}}i{\v{c}}, and Klav{\v{z}}ar. Two players, Dominator and Staller, alternatingly claim vertices of a graph $G$ where Dominator…

Combinatorics · Mathematics 2024-08-02 Ali Deniz Bagdas , Dennis Clemens , Fabian Hamann , Yannick Mogge

We study two positional games played on hypergraphs, whose edges may be interpreted as winning sets. Two players take turns picking a previously unpicked vertex of the hypergraph. We say a player fills an edge if that player has picked all…

Discrete Mathematics · Computer Science 2026-04-14 Florian Galliot

A predominated graph is a pair $(G,D)$, where $G$ is a graph and the vertices in $D\subseteq V(G)$ are considered already dominated. Maker-Breaker domination game critical (MBD critical) predominated graphs are introduced as the…

Combinatorics · Mathematics 2025-03-18 Csilla Bujtás , Pakanun Dokyeesun , Sandi Klavžar , Miloš Stojaković

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…

Combinatorics · Mathematics 2025-07-24 Boštjan Brešar , Tanja Dravec , Kirsti Kuenzel , Douglas F. Rall

The Maker-Breaker domination game is played on a graph $G$ by Dominator and Staller. The players alternatively select a vertex of $G$ that was not yet chosen in the course of the game. Dominator wins if at some point the vertices he has…

Combinatorics · Mathematics 2019-03-14 Valentin Gledel , Vesna Iršič , Sandi Klavžar

We study the parameterized complexity of several positional games. Our main result is that Short Generalized Hex is W[1]-complete parameterized by the number of moves. This solves an open problem from Downey and Fellows' influential list of…

Computational Complexity · Computer Science 2017-04-28 Édouard Bonnet , Serge Gaspers , Antonin Lambilliotte , Stefan Rümmele , Abdallah Saffidine

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…

Combinatorics · Mathematics 2025-12-10 Athira Divakaran , Tijo James , Sandi Klavžar , Latha S Nair

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…

Combinatorics · Mathematics 2022-06-28 Csilla Bujtás , Pakanun Dokyeesun

We study the algorithmic complexity of Maker-Breaker games played on the edge sets of general graphs. We mainly consider the perfect matching game and the $H$-game. Maker wins if she claims the edges of a perfect matching in the first, and…

Computational Complexity · Computer Science 2024-11-18 Eric Duchêne , Valentin Gledel , Fionn Mc Inerney , Nicolas Nisse , Nacim Oijid , Aline Parreau , Miloš Stojaković

In the Maker-Breaker domination game played on a graph $G$, Dominator's goal is to select a dominating set and Staller's goal is to claim a closed neighborhood of some vertex. We study the cases when Staller can win the game. If Dominator…

Combinatorics · Mathematics 2024-02-14 Csilla Bujtás , Pakanun Dokyeesun , Sandi Klavžar

The Maker-Breaker domination game (MBD game) is a two-player game played on a graph $G$ by Dominator and Staller. They alternately select unplayed vertices of $G$. The goal of Dominator is to form a dominating set with the set of vertices…

Combinatorics · Mathematics 2025-12-10 Athira Divakaran , Tanja Dravec , Tijo James , Sandi Klavžar , Latha S Nair

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…

Discrete Mathematics · Computer Science 2025-03-25 Florian Galliot , Sylvain Gravier , Isabelle Sivignon

Given a c-colored graph G, a vertex of G is happy if it has the same color as all its neighbors. The notion of happy vertices was introduced by Zhang and Li to compute the homophily of a graph. Eto, et al. introduced the Maker-Maker version…

Discrete Mathematics · Computer Science 2026-01-13 Mathieu Hilaire , Perig Montfort , Nacim Oijid

We study the Maker-Maker version of the domination game introduced in 2018 by Duch\^ene et al. Given a graph, two players alternately claim vertices. The first player to claim a dominating set of the graph wins. As the Maker-Breaker…

Combinatorics · Mathematics 2023-06-12 Eric Duchêne , Arthur Dumas , Nacim Oijid , Aline Parreau , Eric Rémila
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