Related papers: The Toucher-Isolator game
We introduce and study coverage games - a novel framework for multi-agent planning in settings in which a system operates several agents but does not have full control on them, or interacts with an environment that consists of several…
The domination game is an optimization game played by two players, Dominator and Staller, who alternately select vertices in a graph $G$. A vertex is said to be dominated if it has been selected or is adjacent to a selected vertex. Each…
The slow-coloring game is played by Lister and Painter on a graph $G$. On each round, Lister marks a nonempty subset $M$ of the uncolored vertices, scoring $|M|$ points. Painter then gives a color to a subset of $M$ that is independent in…
A general position set of a graph $G$ is a set of vertices $S$ in $G$ such that no three vertices from $S$ lie on a common shortest path. In this paper we introduce and study the general position achievement game. The game is played on a…
In numerous positional games the identity of the winner is easily determined. In this case one of the more interesting questions is not {\em who} wins but rather {\em how fast} can one win. These type of problems were studied earlier for…
The radius-$r$ splitter game is played on a graph $G$ between two players: Splitter and Connector. In each round, Connector selects a vertex $v$, and the current game arena is restricted to the radius-$r$ neighborhood of $v$. Then Splitter…
We investigate Maker-Breaker games on graphs of size $\aleph_1$ in which Maker's goal is to build a copy of the host graph. We establish a firm dependence of the outcome of the game on the axiomatic framework. Relating to this, we prove…
The localization game is a two player combinatorial game played on a graph $G=(V,E)$. The cops choose a set of vertices $S_1 \subseteq V$ with $|S_1|=k$. The robber then chooses a vertex $v \in V$ whose location is hidden from the cops, but…
Classic reachability games on graphs are zero-sum games, where the goal of one player, Eve, is to visit a vertex from a given target set, and that of other player, Adam, is to prevent this. Generalised reachability games, studied by…
The domination game is played on a graph $G$ by two players, Dominator and Staller, who alternate in selecting vertices until each vertex in the graph $G$ is contained in the closed neighbourhood of the set of selected vertices. Dominator's…
Graph Pebbling is a well-studied single-player game on graphs. We introduce the game of Blocking Pebbles which adapts Graph Pebbling into a two-player strategy game in order to examine it within the context of Combinatorial Game Theory.…
In this paper, we continue the study of the total domination game in graphs introduced in [Graphs Combin. 31(5) (2015), 1453--1462], where the players Dominator and Staller alternately select vertices of $G$. Each vertex chosen must…
The cordiality game is played on a graph $G$ by two players, Admirable (A) and Impish (I), who take turns selecting \track{unlabeled} vertices of $G$. Admirable labels the selected vertices by $0$ and Impish by $1$, and the resulting label…
We analyze the duration of the unbiased Avoider-Enforcer game for three basic positional games. All the games are played on the edges of the complete graph on $n$ vertices, and Avoider's goal is to keep his graph outerplanar, diamond-free…
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…
The containment game is a full information game for two players, initialised with a set of occupied vertices in an infinite connected graph $G$. On the $t$-th turn, the first player, called Spreader, extends the occupied set to $g(t)$…
We study the positional game where two players, Maker and Breaker, alternately select respectively $1$ and $b$ previously unclaimed edges of $K_n$. Maker wins if she succeeds in claiming all edges of some odd cycle in $K_n$ and Breaker wins…
In the Avoider-Enforcer convention of positional games, two players, Avoider and Enforcer, take turns selecting vertices from a hypergraph H. Enforcer wins if, by the time all vertices of H have been selected, Avoider has completely filled…
We combine the ideas of edge coloring games and asymmetric graph coloring games and define the \emph{$(m,1)$-edge coloring game}, which is alternatively played by two players Maker and Breaker on a finite simple graph $G$ with a set of…
We introduce the game of Surrounding Cops and Robbers on a graph, as a variant of the original game of Cops and Robbers. In contrast to the original game in which the cops win by occupying the same vertex as the robber, they now win by…