相关论文: Eternally surrounding a robber

We introduce a cover time problem for random walks on dynamic graphs in which the graph expands in time and the walker moves at random times. Time to cover all nodes and number of returns to original states are analyzed in resulting model.

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 consider a class of pursuit-evasion problems where an evader enters a directed acyclic graph and attempts to reach one of the terminal nodes. A pursuer enters the graph at a later time and attempts to capture the evader before it reaches…

We study a game of pursuit and evasion introduced by Seager in 2012, in which a cop searches the robber from outside the graph, using distance queries. A graph on which the cop wins is called locatable. In her original paper, Seager asked…

The Cops and Robber game is played on undirected finite graphs. $k$ cops and one robber are positioned on vertices and take turn in moving along edges. The cops win if, after a move, a cop and the robber are on the same vertex. A graph is…

A generalization of hyperopic cops and robber, analogous to the $k$-visibility cops and robber, is introduced in this paper. For a positive integer $k$ the $k$-hyperopic game of cops and robber is defined similarly as the usual cops and…

We give logarithmic lower bounds for the approximability of the Minimum Dominating Set problem in connected (alpha,beta)-Power Law Graphs. We give also a best up to now upper approximation bound on the problem for the case of the parameters…

Our goal is to finally settle the persistent problem in Diophantine Approximation of finding best linear approximates. Classical results from the theory of continued fractions provide the solution for the special homogeneous case in the…

We introduce the notion of watching systems in graphs, which is a generalization of that of identifying codes. We give some basic properties of watching systems, an upper bound on the minimum size of a watching system, and results on the…

The ring of graph invariants is spanned by the basic graph invariants which calculate the number of subgraphs isomorphic to a given graph in other graphs. These subgraphs counting invariants are not algebraically independent. In our view…

We investigate a variation of the art gallery problem in which a team of mobile guards tries to track an unpredictable intruder in a simply-connected polygonal environment. In this work, we use the deployment strategy for diagonal guards…

We consider the cop-throttling number of a graph $G$ for the game of Cops and Robbers, which is defined to be the minimum of $(k + \text{capt}_k(G))$, where $k$ is the number of cops and $\text{capt}_k(G)$ is the minimum number of rounds…

We consider the problems of finding optimal identifying codes, (open) locating-dominating sets and resolving sets of an interval or a permutation graph. In these problems, one asks to find a subset of vertices, normally called a…

We consider the problem where an agent wants to find a hidden object that is randomly located in some vertex of a directed acyclic graph (DAG) according to a fixed but possibly unknown distribution. The agent can only examine vertices whose…

We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…

Cops and Robbers is a pursuit evasion game played on a graph, first introduced independently by Quilliot \cite{quilliot1978jeux} and Nowakowski and Winkler \cite{NOWAKOWSKI1983235} over four decades ago. A main interest in recent the…

Let $G=(V,E)$ be a graph. A subset $D\subseteq V$ is a dominating set if every vertex not in $D$ is adjacent to a vertex in $D$. The domination number of $G$, denoted by $\gamma(G)$, is the smallest cardinality of a dominating set of $G$.…

We prove new explicit inapproximability results for the Vertex Cover Problem on the Power Law Graphs and some functional generalizations of that class of graphs. Our results depend on special bounded degree amplifier constructions for those…

The game of cops and robbers is played on a fixed (finite or infinite) graph $G$. The cop chooses his starting position, then the robber chooses his. After that, they take turns and move to adjacent vertices, or stay at their current…

We introduce a new variant of the game of Cops and Robbers played on graphs, where the robber is invisible unless outside the neighbor set of a cop. The hyperopic cop number is the corresponding analogue of the cop number, and we…