Related papers: Avoider-Enforcer Game is NP-hard
In this paper, we study algorithms for special cases of energy games, a class of turn-based games on graphs that show up in the quantitative analysis of reactive systems. In an energy game, the vertices of a weighted directed graph belong…
In this short paper we study the game of cops and robbers, which is played on the vertices of some fixed graph $G$. Cops and a robber are allowed to move along the edges of $G$ and the goal of cops is to capture the robber. The cop number…
The game Arc-Kayles is played on an undirected graph with two players taking turns deleting an edge and its endpoints from the graph. We study a generalization of this game, Weighted Arc Kayles (WAK for short), played on graphs with…
In a pursuit-evasion game, a team of pursuers attempt to capture an evader. The players alternate turns, move with equal speed, and have full information about the state of the game. We consider the most restictive capture condition: a…
Consider an undirected graph modeling a social network, where the vertices represent users, and the edges do connections among them. In the competitive diffusion game, each of a number of players chooses a vertex as a seed to propagate…
We generalise the popular cops and robbers game to multi-layer graphs, where each cop and the robber are restricted to a single layer (or set of edges). We show that initial intuition about the best way to allocate cops to layers is not…
In the recently introduced network patrolling game, an Attacker carries out an attack on a node of her choice, for a given number m of consecutive periods. The parameter m indicates the difficulty of the attack at a given node. To thwart…
We investigate the complexity of finding a winning strategy for the mis\`ere version of three games played on graphs : two variants of the game $\text{NimG}$, introduced by Stockmann in 2004 and the game $\text{Vertex Geography}$ on both…
Let $H = (V,E)$ be a hypergraph with vertex set $V$ and edge set $E$ of order $\nH = |V|$ and size $\mH = |E|$. A transversal in $H$ is a subset of vertices in $H$ that has a nonempty intersection with every edge of $H$. A vertex hits an…
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…
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…
Temporal graphs extend ordinary graphs with discrete time that affects the availability of edges. We consider solving games played on temporal graphs where one player aims to explore the graph, i.e., visit all vertices. The complexity…
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 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…
Player ONE chooses a meager set and player TWO, a nowhere dense set per inning. They play $\omega$ many innings. ONE's consecutive choices must form a (weakly) increasing sequence. TWO wins if the union of the chosen nowhere dense sets…
In the game of Cops and Robbers, a team of cops attempts to capture a robber on a graph $G$. All players occupy vertices of $G$. The game operates in rounds; in each round the cops move to neighboring vertices, after which the robber does…
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 $(a:b)$…
We consider a variant of Cops and Robbers in which both the cops and the robber are allowed to traverse up to $s$ edges on each of their turns, where $s \ge 2$. We give several general for this new model as well as establish bounds for the…
Originating in evolutionary game theory, the class of "zero-determinant" strategies enables a player to unilaterally enforce linear payoff relationships in simple repeated games. An upshot of this kind of payoff constraint is that it can…
We study the m-eternal domination problem from the perspective of the attacker. For many graph classes, the minimum required number of guards to defend eternally is known. By definition, if the defender has less than the required number of…