English
Related papers

Related papers: Thresholds for the biased Maker-Breaker domination…

200 papers

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

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

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 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

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 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

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

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 (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

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

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

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 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

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 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

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

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…

Combinatorics · Mathematics 2014-11-20 Csilla Bujtás , Zsolt Tuza

We study the $(a:b)$ Maker-Breaker subgraph game played on the edges of the complete graph $K_n$ on $n$ vertices, $n,a,b \in \mathbb{N}$ where the goal of Maker is to build a copy of a specific fixed subgraph $H$. In our work this is a…

Combinatorics · Mathematics 2024-06-18 Adnane Fouadi , Mourad El Ouali , Anand Srivastav

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
‹ Prev 1 2 3 10 Next ›