Related papers: Maker-Breaker Percolation Games I: Crossing Grids

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…

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…

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…

Given an integer-valued matrix $A$ of dimension $\ell \times k$ and an integer-valued vector $b$ of dimension $\ell$, the Maker-Breaker $(A,b)$-game on a set of integers $X$ is the game where Maker and Breaker take turns claiming previously…

A large class of Positional Games are defined on the complete graph on $n$ vertices. The players, Maker and Breaker, take the edges of the graph in turns, and Maker wins iff his subgraph has a given -- usually monotone -- property. Here we…

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…

For positive integers $n$ and $q$ and a monotone graph property $\cA$, we consider the two player, perfect information game $\WC(n,q,\cA)$, which is defined as follows. The game proceeds in rounds. In each round, the first player, called…

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…

Let $d(x,y)$ denote the length of a shortest path between vertices $x$ and $y$ in a graph $G$ with vertex set $V$. For a positive integer $k$, let $d_k(x,y)=\min\{d(x,y), k+1\}$ and $R_k\{x,y\}=\{z\in V: d_k(x,z) \neq d_k(y,z)\}$. A set $S…

We study the Maker-Breaker $H$-game played on the edge set of the random graph $G_{n,p}$. In this game two players, Maker and Breaker, alternately claim unclaimed edges of $G_{n,p}$, until all the edges are claimed. Maker wins if he claims…

In this paper, we study Maker-Breaker games on the random hypergraph $H_{n,s,p}$, obtained from the complete $s$-graph by keeping every edge independently with probability $p$. We determine the threshold probability for the property of…

We introduce and study Maker/Breaker-type positional games on random graphs. Our main concern is to determine the threshold probability $p_{F}$ for the existence of Maker's strategy to claim a member of $F$ in the unbiased game played on…

In a Maker-Breaker game there are two players, Maker and Breaker, where Maker wins if they create a specified structure while Breaker wins if they prevent Maker from winning indefinitely. A $3$-term arithmetic progression, or $3$-AP, is a…

In this paper we study the (a : b) Maker-Breaker Connectivity game, played on the edge-set of the complete graph on n vertices. We determine the winner for almost all values of a and b.

We study the positional game where two players, Maker and Breaker, alternately select respectively $1$ and $b$ previously unclaimed edges of $K_n$. Maker wins if she succeeds in claiming all edges of some odd cycle in $K_n$ and Breaker wins…

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…

We study two-player positional games where Maker and Breaker take turns to select a previously unoccupied number in $\{1,2,\ldots,n\}$. Maker wins if the numbers selected by Maker contain a solution to the equation \[…

We study the biased $(2:b)$ Walker--Breaker games, played on the edge set of the complete graph on $n$ vertices, $K_n$. These games are a variant of the Maker--Breaker games with the restriction that Walker (playing the role of Maker) has…

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…

For a tree T on n vertices, we study the Maker-Breaker game, played on the edge set of the complete graph on n vertices, which Maker wins as soon as the graph she builds contains a copy of T. We prove that if T has bounded maximum degree,…