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Related papers: Maker-Breaker domination number

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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

The Maker-Breaker total domination number, $\gamma_{\rm MBT}(G)$, of a graph $G$ is introduced as the minimum number of moves of Dominator to win the Maker-Breaker total domination game, provided that he has a winning strategy and is the…

Combinatorics · Mathematics 2025-07-24 Athira Divakaran , Tijo James , Sandi Klavžar , Latha S Nair

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 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

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

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…

Combinatorics · Mathematics 2024-04-17 Jovana Forcan , Jiayue Qi

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 (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

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

A set of vertices $W$ of a graph $G$ is a resolving set if every vertex of $G$ is uniquely determined by its vector of distances to $W$. In this paper, the Maker-Breaker resolving game is introduced. The game is played on a graph $G$ by…

Combinatorics · Mathematics 2020-05-28 Cong X. Kang , Sandi Klavžar , Ismael G. Yero , Eunjeong Yi

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

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

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…

Combinatorics · Mathematics 2013-07-23 Boštjan Brešar , Paul Dorbec , Sandi Klavžar , Gašper Košmrlj

In the $(a,b)$-biased Maker-Breaker domination game, two players alternately select unplayed vertices in a graph $G$ such that Dominator selects $a$ and Staller selects $b$ vertices per move. Dominator wins if the vertices he selected…

Combinatorics · Mathematics 2025-10-29 Boštjan Brešar , Csilla Bujtás , Pakanun Dokyeesun , Tanja Dravec

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

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…

Discrete Mathematics · Computer Science 2014-05-02 Hovhannes G. Tananyan

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

Motivated by the success of domination games and by a variation of the coloring game called the indicated coloring game, we introduce a version of domination games called the indicated domination game. It is played on an arbitrary graph $G$…

Combinatorics · Mathematics 2024-03-28 Boštjan Brešar , Csilla Bujtás , Vesna Iršič , Douglas F. Rall , Zsolt Tuza

In the domination game, introduced by Bre\v{s}ar, Klav\v{z}ar and Rall in 2010, Dominator and Staller alternately select a vertex of a graph $G$. A move is legal if the selected vertex $v$ dominates at least one new vertex -- that is, if we…

Combinatorics · Mathematics 2014-07-01 Csilla Bujtás

Since its introduction as a Maker-Breaker positional game by Duch\^ene et al. in 2020, the Maker-Breaker domination game has become one of the most studied positional games on vertices. In this game, two players, Dominator and Staller,…

Combinatorics · Mathematics 2026-01-14 Guillaume Bagan , Mathieu Hilaire , Nacim Oijid , Aline Parreau
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