Related papers: The multi-robber damage number of a graph

This paper considers a game in which a single cop and a single robber take turns moving along the edges of a given graph $G$. If there exists a strategy for the cop which enables it to be positioned at the same vertex as the robber…

The game of Cops and Robbers on graphs is a well-studied pursuit--evasion model whose central parameter, the cop number, captures the minimum number of pursuers required to guarantee capture of an adversary on a given graph. While the cop…

We consider a variant of the game of Cops and Robbers, called Containment, in which cops move from edge to adjacent edge, the robber moves from vertex to adjacent vertex (but cannot move along an edge occupied by a cop). The cops win by…

We study the entanglement game, which is a version of cops and robbers, on sparse graphs. While the minimum degree of a graph G is a lower bound for the number of cops needed to catch a robber in G, we show that the required number of cops…

We explore a variant of the game of Cops and Robber introduced by Bonato et al.~where the robber is invisible unless outside the common neighbourhood of the cops. The hyperopic cop number is analogous to the cop number and we investigate…

In the ordinary version of the pursuit-evasion game "cops and robbers", a team of cops and a robber occupy vertices of a graph and alternately move along the graph's edges, with perfect information about each other. If a cop lands on the…

In the game of Cops and Robbers, one of the most useful results is that an isometric path in a graph can be guarded by one cop. In this paper, we introduce the concept of wide shadow in a subgraph, and use it to characterize all 1-guardable…

The game of cops and robber has been studied for many years. Denoting $\mathsf{Forb}(4K_1)$ to be the family of all graphs that contain no induced subgraph isomorphic to $4K_1$ (e.g., with independence number less than $4$), we prove that…

We survey results at the intersection of topological graph theory and the game of Cops and Robbers, focusing on results, conjectures, and open problems for the cop number of a graph embedded on a surface. After a discussion on results for…

The game of Cops and Robbers is a pursuit-evasion game on graphs that has been extensively studied in finite settings, particularly through the concept of cop number. In this paper, we explore infinite variants of the game, focusing on the…

We introduce a new game played on graphs, ``Agents and Adversary". This game is reminiscent of ``Cops and Robbers" but has some fundamental differences. We classify infinite families of graphs as Agents-win and Adversary-win. We then define…

We study the zero-visibility cops and robbers game, where the robber is invisible to the cops until they are caught. This differs from the classic game where full information about the robber's location is known at any time. A previously…

Introduced by Harris, Insko, Prieto Langarica, Stoisavljevic, and Sullivan, the \emph{tipsy cop and drunken robber} is a variant of the cop and robber game on graphs in which the robber simply moves randomly along the graph, while the cop…

We investigate a pursuit-evasion game on an undirected graph in which a robber, moving at a fixed constant speed, attempts to evade a team of cops who are blind to the robber's location and can quickly travel between any pair of vertices in…

We consider a variant of the Cops and Robber game, introduced by Fomin, Golovach, Kratochvil, in which the robber has unbounded speed, i.e. can take any path from her vertex in her turn, but she is not allowed to pass through a vertex…

In this paper we analyze and model three open problems posed by Harris, Insko, Prieto-Langarica, Stoisavljevic, and Sullivan in 2020 concerning the tipsy cop and robber game on graphs. The three different scenarios we model account for…

We consider the Cops and Robber pursuit-evasion game when the edge-set of the graph is allowed to change in time, possibly at every round. Specifically, the game is played on an infinite periodic sequence $\mathcal{G} = (G_0, \dots,…

We introduce and study quantized versions of Cop and Robber game. We achieve this by using graph-preserving quantum operations, which are the quantum analogues of stochastic operations preserving the graph. We provide the tight bound for…

We consider a game in which a cop searches for a moving robber on a graph using distance probes, which is a slight variation on one introduced by Seager. Carragher, Choi, Delcourt, Erickson and West showed that for any n-vertex graph $G$…

"Zombies and Survivor" is a variant of the well-studied game of "Cops and Robber" where the zombies (cops) can only move closer to the survivor (robber). We consider the deterministic version of the game where a zombie can choose their path…