Related papers: Spanning Structures in Walker--Breaker Games

We introduce a new positional game called `Toucher-Isolator', which is a quantitative version of a Maker-Breaker type game. The playing board is the set of edges of a given graph G, and the two players, Toucher and Isolator, claim edges…

We study the $(p,q)$-Maker Breaker Crossing game introduced by Day and Falgas Ravry in 'Maker-Breaker percolation games I: crossing grids'. The game described in their paper involves two players Maker and Breaker who take turns claiming p…

We study Maker/Breaker games on the edges of sparse graphs. Maker and Breaker take turns in claiming previously unclaimed edges of a given graph H. Maker aims to occupy a given target graph G and Breaker tries to prevent Maker from…

In the $\left(1:b\right)$ component game played on a graph $G$, two players, Maker and Breaker, alternately claim~$1$ and~$b$ previously unclaimed edges of $G$, respectively. Maker's aim is to maximise the size of a largest connected…

Two new versions of the so-called Maker-Breaker Positional Games are defined by J\'ozsef Beck in [{\em Combinatorica} {\bf 22}(2) (2002) 169--216]. He defines two players, Picker and Chooser. In each round, Picker takes a pair of elements…

The triangle game introduced by Chv\'{a}tal and Erd\H{o}s (1978) is one of the most famous combinatorial games. For $n,q\in\mathbb{N}$, the $(n,q)$-triangle game is played by two players, called Maker and Breaker, on the complete graph…

Motivated by problems in percolation theory, we study the following 2-player positional game. Let $\Lambda_{m \times n}$ be a rectangular grid-graph with $m$ vertices in each row and $n$ vertices in each column. Two players, Maker and…

We introduce a new two-player game on graphs, in which players alternate choosing vertices until the set of chosen vertices forms a dominating set. The last player to choose a vertex is the winner. The game fits into the scheme of several…

In the Oriented-cycle game, introduced by Bollob\'as and Szab\'o, two players, called OMaker and OBreaker, alternately direct edges of $K_n$. OMaker directs exactly one edge, whereas OBreaker is allowed to direct between one and $b$ edges.…

Given a tree $T=(V,E)$ on $n$ vertices, we consider the $(1 : q)$ Maker-Breaker tree embedding game ${\mathcal T}_n$. The board of this game is the edge set of the complete graph on $n$ vertices. Maker wins ${\mathcal T}_n$ if and only if…

In the Constructor-Blocker game, two players, Constructor and Blocker, alternatively claim unclaimed edges of the complete graph $K_n$. For given graphs $F$ and $H$, Constructor can only claim edges that leave her graph $F$-free, while…

The Maker-Breaker resolving game is a game played on a graph $G$ by Resolver and Spoiler. The players taking turns alternately in which each player selects a not yet played vertex of $G$. The goal of Resolver is to select all the vertices…

One of the main objective of this paper is to relate Beck's conjecture for k-in-a-row games. The conjecture states that playing on the same board Picker is better off in a Chooser-Picker game than the second player in the Maker-Breaker…

Consider the following game played by Maker and Breaker on the vertices of the cycle $C_{n}$, with first move given to Breaker. The aim of Maker is to maximise the number of adjacent pairs of vertices that are both claimed by her, and the…

In numerous positional games the identity of the winner is easily determined. In this case one of the more interesting questions is not {\em who} wins but rather {\em how fast} can one win. These type of problems were studied earlier for…

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…

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 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…

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…

In a biased weak $(a,b)$ polyform achievement game, the maker and the breaker alternately mark $a,b$ previously unmarked cells on an infinite board, respectively. The maker's goal is to mark a set of cells congruent to a polyform. The…