Related papers: Maker-Breaker Percolation Games II: Escaping to In…
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…
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…
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…
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…
This paper introduced a pursuit and evasion game to be played on a connected graph. One player moves invisibly around the graph, and the other player must guess his position. At each time step the second player guesses a vertex, winning if…
We study two types of two player, perfect information games with no chance moves, played on the edge set of the binomial random graph ${\mathcal G}(n,p)$. In each round of the $(1 : q)$ Waiter-Client Hamiltonicity game, the first player,…
In a Take-Away Game on hypergraphs, two players take turns to remove the vertices and the hyperedges of the hypergraphs. In each turn, a player must remove either a single vertex or a hyperedge. When a player chooses to remove one vertex,…
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…
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,…
Graph burning is a discrete-time process that models the spread of influence in a network. Vertices are either burning or unburned, and in each round, a burning vertex causes all of its neighbours to become burning before a new fire source…
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…
In the Maker-Breaker vertex colouring game, first publicised by Gardner in 1981, Maker and Breaker alternately colour vertices of a graph using a fixed palette, maintaining a proper colouring at all times. Maker aims to colour the whole…
We introduce a model involving two adversaries Buster and Fixer taking turns modifying a connected graph, where each round consists of Buster deleting a subset of edges and Fixer responding by adding edges from a finite reserve set of…
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…
We consider a stochastic game of control and stopping specified in terms of a process $X_t=-\theta \Lambda_t+W_t$, representing the holdings of Player 1, where $W$ is a Brownian motion, $\theta$ is a Bernoulli random variable indicating…
We consider a variation on Maker-Breaker games on graphs or digraphs where the edges have random costs. We assume that Maker wishes to choose the edges of a spanning tree, but wishes to minimise his cost. Meanwhile Breaker wants to make…
Given a fixed graph $H$ with at least two edges and positive integers $n$ and $b$, the strict $(1 \colon b)$ Avoider-Enforcer $H$-game, played on the edge set of $K_n$, has the following rules: In each turn Avoider picks exactly one edge,…
Consider the following probabilistic one-player game: The board is a graph with $n$ vertices, which initially contains no edges. In each step, a new edge is drawn uniformly at random from all non-edges and is presented to the player,…
Two-player games on graphs are widely studied in formal methods as they model the interaction between a system and its environment. The game is played by moving a token throughout a graph to produce an infinite path. There are several…
Cops and robbers is a game between two players, where one tries to catch the other by moving along the edges of a graph. It is well known that on a finite graph the cop has a winning strategy if and only if the graph is constructible and…