In the cops and robber game, two players play alternately by moving their tokens along the edges of a graph. The first one plays with the cops and the second one with one robber. The cops aim at capturing the robber, while the robber tries to infinitely evade the cops. The main problem consists in minimizing the number of cops used to capture the robber in a graph. This minimum number is called...

The effect of irradiation and packaging conditions on the content of cholesterol oxidation products (COPs) and lipid oxidation in cooked turkey, beef, and pork during storage was studied. Ground turkey leg, beef, and pork were cooked, packaged either in oxygen-permeable or oxygen-impermeable bags, and irradiated at 0 or 4.5 kGy. Lipid oxidation and COPs were determined after 0 and 7 days of sto...

We prove that n cops can capture (that is, some cop can get less than unit distance from) a robber in a continuous square region with side length less than √ 5n and hence that bn/ √ 5c+ 1 cops can capture a robber in a square with side length n. We extend these results to three dimensions, proving that 0.34869 · · ·n2 +O(n) cops can capture a robber in a n× n× n cube and that a robber can forev...

The game of cops and robbers is played with a set of 'cops' and a 'robber' who occupy some vertices of a graph. Both sides have perfect information and they move alternately to adjacent vertices. The robber is captured if at least one of the cops occupies the same vertex as the robber. The problem is to determine on a given graph, G, the least number of cops sufficient to capture the robber, ca...

In [1] Aigner and Fromme and in [10] Quilliot studied the following game, called cops and robbers. There is a finite, connected, undirected graph G = (V, E), m cops and one robber. First the cops choose one vertex each as initial position. Next the robber makes his choice. Afterwards they move alternately (first the cops, then the robber) along the edges of the graph or stay. Denote by c(G) the...

The experience described in this paper is being developed in the framework of the PALETTE1 project by two teams of researchers involved in collecting information from some Communities of practice2 (CoPs) then in providing this information through suitable formats to their technical partners in the aim of designing an interoperable and extensible set of innovative services and specific scenarios...

BACKGROUND Healthcare organisations seeking to manage knowledge and improve organisational performance are increasingly investing in communities of practice (CoPs). Such investments are being made in the absence of empirical evidence demonstrating the impact of CoPs in improving the delivery of healthcare. A realist evaluation is proposed to address this knowledge gap. Underpinned by the princi...

In this paper, we study the vertex pursuit game of Cops and Robbers where cops try to capture a robber on the vertices of the graph. The minimum number of cops required to win on a given graph G is the cop number of G. We present asymptotic results for the game of Cops and Robber played on a random graph G(n, p) for a wide range of p = p(n). It has been shown that the cop number as a function o...

Geo-replicated, distributed data stores that support complex online applications, such as social networks, must provide an “alwayson” experience where operations always complete with low latency. Today’s systems often sacrifice strong consistency to achieve these goals, exposing inconsistencies to their clients and necessitating complex application logic. In this paper, we identify and define a...

We consider a variation of the Cops and Robber game where the cops can only see the robber when the distance between them is at most a fixed parameter `. We consider the basic consequences of this definition for some simple graph families, and show that this model is not monotonic, unlike common models where the robber is invisible. We see that cops’ strategy consists of a phase in which they n...