Related papers: The $K^4$-Game
A subset of the vertex set of a graph is geodetically convex if it contains every vertex on any shortest path between two elements of the subset. The convex hull of a set of vertices is the smallest convex set containing the set. We study…
In this paper we introduce and study the domination game on hypergraphs. This is played on a hypergraph $\mathcal{H}$ by two players, namely Dominator and Staller, who alternately select vertices such that each selected vertex enlarges the…
We analyze a coin-based game with two players where, before starting the game, each player selects a string of length $n$ comprised of coin tosses. They alternate turns, choosing the outcome of a coin toss according to specific rules. As a…
This paper considers a class of two-player zero-sum games on directed graphs whose vertices are equipped with random payoffs of bounded support known by both players. Starting from a fixed vertex, players take turns to move a token along…
In the tournament game two players, called Maker and Breaker, alternately take turns in claiming an unclaimed edge of the complete graph on n vertices and selecting one of the two possible orientations. Before the game starts, Breaker fixes…
A positional game is a game where two players sequentially label vertices of a hypergraph, consisting of a board and a collection of winning sets, with colors assigned to each player until all vertices of the board are claimed. The first…
For a finite set $X$, a family of sets ${\mathcal F} \subseteq 2^X$ and a positive integer $q$, we consider two types of two player, perfect information games with no chance moves. In each round of the $(1 : q)$ Waiter-Client game $(X,…
We consider games played on finite graphs, whose goal is to obtain a trace belonging to a given set of winning traces. We focus on those states from which Player 1 cannot force a win. We explore and compare several criteria for establishing…
In this paper, we introduce a graph coloring game called the Edge-Distinguishing Game (EDGe). The edge-distinguishing chromatic number of a graph is used to determine the moves each player can make. We determine which player has a winning…
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…
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 $q+1$…
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 study a combinatorial game derived from a problem in the German National Mathematics Competition. In this game, two players take turns removing numbers from a finite set of natural numbers, aiming to satisfy a certain divisibility…
A partially parallel dynamical noisy binary choice (Ising) game in discrete time of $N$ players on complete graphs with $k$ players having a possibility of changing their strategies at each time moment called $k$-flip Ising game is…
In chomp on graphs, two players alternatingly pick an edge or a vertex from a graph. The player that cannot move any more loses. The questions one wants to answer for a given graph are: Which player has a winning strategy? Can a explicit…
Given a graph G with n vertices and k players, each of which is placing a facility on one of the vertices of G, we define the score of the i'th player to be the number of vertices for which, among all players, the facility placed by the…
We examine two-player games over finite weighted graphs with quantitative (mean-payoff or energy) objective, where one of the players additionally needs to satisfy a fairness objective. The specific fairness we consider is called 'strong…
The Strong Ramsey game $\mathcal{R}(B,G)$ is a two player game with players $P_1$ and $P_2$, where $B$ and $G$ are $k$-uniform hypergraphs for some $k \geq 2$. $G$ is always finite, while $B$ may be infinite. $P_1$ and $P_2$ alternately…
Node Kayles is a well-known two-player impartial game on graphs: Given an undirected graph, each player alternately chooses a vertex not adjacent to previously chosen vertices, and a player who cannot choose a new vertex loses the game. The…
In this paper, we introduce a two-player impartial game on graphs, called a {\em feedback game}, which is a variant of the generalized geography. We study the feedback game on Eulerian graphs. In particular, we show that the…