Related papers: Tree universality in positional games
By now, the Maker-Breaker connectivity game on a complete graph $K_n$ or on a random graph $G\sim G_{n,p}$ is well studied. Recently, London and Pluh\'ar suggested a variant in which Maker always needs to choose her edges in such a way that…
We initiate the study of the phantom version of Maker-Breaker positional games. In a phantom game, the moves of one of the players are hidden from the other player, who still has the complete information. We look at the biased $(a:b)$…
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…
We study biased Maker-Breaker positional games between two players, one of whom is playing randomly against an opponent with an optimal strategy. In this paper we consider the scenario when Maker plays randomly and Breaker is "clever", and…
We introduce a general framework for positional games in which players score points by claiming a prescribed portion of each winning set, extending the notion of scoring Maker-Breaker games. In the scoring variant, Maker gains a point by…
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…
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…
We present constructions regarding the general behaviour of biased positional games, and amongst others show that the outcome of such a game can differ in an arbitrary way depending on which player starts the game, and that fair biased…
In the Maker-Breaker positional game, Maker and Breaker take turns picking vertices of a hypergraph $H$, and Maker wins if and only if she possesses all the vertices of some edge of $H$. Deciding the outcome (i.e. which player has a winning…
Maker-Breaker subgraph games are among the most famous combinatorial games. For given $n,q \in \mathbb{N}$ and a subgraph $C$ of the complete graph $K_n$, the two players, called Maker and Breaker, alternately claim edges of $K_n$. In each…
We study biased {\em orientation games}, in which the board is the complete graph $K_n$, and Maker and Breaker take turns in directing previously undirected edges of $K_n$. At the end of the game, the obtained graph is a tournament. Maker…
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 study Maker/Breaker games on the edges of the complete graph, as introduced by Chvatal and Erdos. We show that in the (m:b) clique game played on K_{N}, the complete graph on N vertices, Maker can achieve a K_{q} for q = (m/(log_{2}(b +…
We study the Maker-Breaker tournament game played on the edge set of a given graph $G$. Two players, Maker and Breaker claim unclaimed edges of $G$ in turns, and Maker wins if by the end of the game she claims all the edges of a pre-defined…
We study biased Maker-Breaker games on a graph system $\{G_1,\ldots,G_s\}$, in which Maker's goal is to claim certain rainbow structures, i.e., specified subgraphs consisting of at most one edge from each graph $G_i$. We consider the…
We consider the Maker-Breaker positional game on the vertices of the $n$-dimensional hypercube $\{0,1\}^n$ with $k$-dimensional subcubes as winning sets. We describe a pairing strategy which allows Breaker to win if $n$ is a power of 4 and…
This paper considers a game version of the general position problem in which a general position set is built through adversarial play. Two players in a graph, Builder and Blocker, take it in turns to add a vertex to a set, such that the…
We study two positional games played on hypergraphs, whose edges may be interpreted as winning sets. Two players take turns picking a previously unpicked vertex of the hypergraph. We say a player fills an edge if that player has picked all…
In a $(1:b)$ biased Maker-Breaker game, how good a strategy is for a player can be measured by the bias range for which its rival can win, choosing an appropriate counterstrategy. Bednarska and {\L}uczak proved that, in the $H$-subgraph…
For a graph G, a monotone increasing graph property P and positive integer q, we define the Client-Waiter game to be a two-player game which runs as follows. In each turn Waiter is offering Client a subset of at least one and at most q+1…