Related papers: The Localization Game On Cartesian Products
We bound expected capture time and throttling number for the cop versus gambler game on a connected graph with $n$ vertices, a variant of the cop versus robber game that is played in darkness, where the adversary hops between vertices using…
A set of vertices $W$ of a graph $G$ is a resolving set if every vertex of $G$ is uniquely determined by its vector of distances to $W$. In this paper, the Maker-Breaker resolving game is introduced. The game is played on a graph $G$ by…
We consider the cops and robber game variant consisting of one cop and one robber on time-varying graphs (TVG). The considered TVGs are edge periodic graphs, i.e., for each edge, a binary string $s_e$ determines in which time step the edge…
A team of $r$ {\it revolutionaries} and a team of $s$ {\it spies} play a game on a graph $G$. Initially, revolutionaries and then spies take positions at vertices. In each subsequent round, each revolutionary may move to an adjacent vertex…
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…
We examine a version of the Cops and Robber (CR) game in which the robber is invisible, i.e., the cops do not know his location until they capture him. Apparently this game (CiR) has received little attention in the CR literature. We…
We consider the well-studied cops and robbers game in the context of oriented graphs, which has received surprisingly little attention to date. We examine the relationship between the cop numbers of an oriented graph and its underlying…
We consider the game of Cops and Robber played on the Cartesian product of two trees. Assuming the players play perfectly, it is shown that if there are two cops in the game, then the length of the game (known as the 2-capture time of the…
The cop throttling number $th_c(G)$ of a graph $G$ for the game of Cops and Robbers is the minimum of $k + capt_k(G)$, where $k$ is the number of cops and $capt_k(G)$ is the minimum number of rounds needed for $k$ cops to capture the robber…
We present two efficient algorithms that compute the optimal strategy for cop in the game of Cop v.s. Gambler where the gambler's strategy is not optimal but known to the cop. The first algorithm is analogous to Bellman-Ford algorithm for…
We present two zero-sum games modeling situations where one player attacks (or hides in) a finite dimensional nonempty compact set, and the other tries to prevent the attack (or find him). The first game, called patrolling game, corresponds…
This paper considers a natural ruleset for playing a partisan combinatorial game on a directed graph, which we call Digraph Placement. Given a digraph $G$ with a not necessarily proper $2$-coloring of $V(G)$, the Digraph Placement game…
We consider a variant of the game of Cops and Robbers, called Lazy Cops and Robbers, where at most one cop can move in any round. We investigate the analogue of the cop number for this game, which we call the lazy cop number. Lazy Cops and…
M\"uller games form a well-established class of games for model checking and verification. These games are played on directed graphs $\mathcal G$ where Player 0 and Player 1 play by generating an infinite path through the graph. The winner…
Several variants of the cops and robbers (CR) game have been studied in the past. In this paper we examine a novel variant, which is played between two cops, each one independently trying to catch a "passive robber". We will call this the…
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…
In a Maker-Breaker game on a graph $G$, Breaker and Maker alternately claim edges of $G$. Maker wins if, after all edges have been claimed, the graph induced by his edges has some desired property. We consider four Maker-Breaker games…
We investigate extremal graphs related to the game of Cops and Robbers. We focus on graphs where a single cop can catch the robber; such graphs are called cop-win. The capture time of a cop-win graph is the minimum number of moves the cop…
In the Hunters and Rabbit game, $k$ hunters attempt to shoot an invisible rabbit on a given graph $G$. In each round, the hunters select $k$ vertices to shoot at, while the rabbit moves along an edge of $G$. The hunters win if, at any…
We introduce and study the Generalized Cops and Robbers game (GCR), an N-player pursuit game in graphs. The two-player version is essentially equivalent to the classic Cops and Robbers (CR) game. The three-player version can be understood…