相关论文: Chain-making games in grid-like posets

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,…

In this paper, we construct two hypergraphs which exhibit the following properties. We first construct a hypergraph $G_{CP}$ and show that Breaker wins the Maker-Breaker game on $G_{CP}$, but Chooser wins the Chooser-Picker game on…

Conway Checkers is a game played with a checker placed in each square of the lower half of an infinite checkerboard. Pieces move by jumping over an adjacent checker, removing the checker jumped over. Conway showed that it is not possible to…

In this paper we consider positional games where the winning sets are tree universal graphs. Specifically, we show that in the unbiased Maker-Breaker game on the complete graph $K_n$, Maker has a strategy to occupy a graph which contains…

We initiate the study of a new variant of the Maker-Breaker positional game, which we call multistage game. Given a hypergraph $\mathcal{H}=(\mathcal{X},\mathcal{F})$ and a bias $b \ge 1$, the $(1:b)$ multistage Maker-Breaker game on…

We introduce and analyze the Walker-Breaker game, a variant of Maker-Breaker games where Maker is constrained to choose edges of a walk or path in a given graph G, with the goal of visiting as many vertices of the underlying graph as…

Given a graph $G$ and $k \in \mathbb{N}$, we introduce the following game played in $G$. Each round, Alice colours an uncoloured vertex of $G$ red, and then Bob colours one blue (if any remain). Once every vertex is coloured, Alice wins if…

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,…

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…

We prove that for each $D\ge 2$ there exists $c>0$ such that whenever $b\le c\big(\tfrac{n}{\log n}\big)^{1/D}$, in the $(1:b)$ Maker-Breaker game played on $E(K_n)$, Maker has a strategy to guarantee claiming a graph $G$ containing copies…

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…

We propose a generalization of positional games, supplementing them with a restriction on the order in which the elements of the board are allowed to be claimed. We introduce poset positional games, which are positional games with an…

The Maker-Breaker connectivity game and Hamilton cycle game belong to the best studied games in positional games theory, including results on biased games, games on random graphs and fast winning strategies. Recently, the Connector-Breaker…

In a Maker-Breaker game on a graph $G$, Breaker and Maker alternately claim edges of $G$. Maker wins if, after all edges have been claimed, the graph induced by his edges has some desired property. We consider four Maker-Breaker games…

On-line chain partition is a two-player game between Spoiler and Algorithm. Spoiler presents a partially ordered set, point by point. Algorithm assigns incoming points (immediately and irrevocably) to the chains which constitute a chain…

We study the biased $(1:b)$ Maker--Breaker positional games, played on the edge set of the complete graph on $n$ vertices, $K_n$. Given Breaker's bias $b$, possibly depending on $n$, we determine the bounds for the minimal number of moves,…

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…

For a positive integer $k$ we consider the $k$-vertex-connectivity game, played on the edge set of $K_n$, the complete graph on $n$ vertices. We first study the Maker-Breaker version of this game and prove that, for any integer $k \geq 2$…

We study the following Maker/Breaker game. Maker and Breaker take turns in choosing vertices from a given n-uniform hypergraph F, with Maker going first. Maker's goal is to completely occupy a hyperedge and Breaker tries to avoid this. Beck…

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…