Related papers: Connector-Breaker games on random boards
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 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…
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…
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…
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 look at the unbiased Maker-Breaker Hamiltonicity game played on the edge set of a complete graph $K_n$, where Maker's goal is to claim a Hamiltonian cycle. First, we prove that, independent of who starts, Maker can win the game for $n =…
In this paper we consider biased Maker-Breaker games played on the edge set of a given graph $G$. We prove that for every $\delta>0$ and large enough $n$, there exists a constant $k$ for which if $\delta(G)\geq \delta n$ and $\chi(G)\geq…
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…
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…
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,…
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 present new results on Maker-Breaker games arising from the Erd\H{o}s-Szekeres problem in planar geometry. This classical problem asks how large a set in general position has to be to ensure the existence of $n$ points that are the…
In this short note we consider a variation of the connectivity Waiter-Client game $WC(n,q,\mathcal{A})$ played on an $n$-vertex graph $G$ which consists of $q+1$ disjoint spanning trees. In this game in each round Waiter offers Client $q+1$…
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 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…
We study the two-player game where Maker and Breaker alternately color the edges of a given graph $G$ with $k$ colors such that adjacent edges never get the same color. Maker's goal is to play such that at the end of the game, all edges are…
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…
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…
We introduce a new type of positional games, played on a vertex set of a graph. Given a graph $G$, two players claim vertices of $G$, where the outcome of the game is determined by the subgraphs of $G$ induced by the vertices claimed by…
We study the $b$-biased Oriented-cycle game where two players, OMaker and OBreaker, take turns directing the edges of $K_n$ (the complete graph on $n$ vertices). In each round, OMaker directs one previously undirected edge followed by…