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Related papers: Maker-Breaker total domination number

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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

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, 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 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

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 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 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 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 total domination game is a two-person competitive optimization game, where the players, Dominator and Staller, alternately select vertices of an isolate-free graph $G$. Each vertex chosen must strictly increase the number of vertices…

Combinatorics · Mathematics 2017-06-06 Csilla Bujtás

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

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

In the total domination game played on a graph $G$, players Dominator and Staller alternately select vertices of $G$, as long as possible, such that each vertex chosen increases the number of vertices totally dominated. Dominator (Staller)…

Combinatorics · Mathematics 2017-09-19 Michael A. Henning , Sandi Klavžar , Douglas F. Rall

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 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

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

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

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

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…

Combinatorics · Mathematics 2016-09-13 Michael A. Henning , Douglas F. Rall

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 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
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