Cops and robbers on graphs and hypergraphs

Cops and Robbers is a vertex-pursuit game played on a graph where a set of cops attempts to capture a robber. Meyniel's Conjecture gives as asymptotic upper bound on the cop number, the number of cops required to win on a connected graph. The incidence graphs of affine planes meet this bound from below, they are called Meyniel extremal. The new parameters mқ and Mқ describe the minimum orders of k-cop-win graphs. The relation of these parameters to Meyniel's Conjecture is discussed. Further, the cop number for all connected graphs of order 10 or less is given. Finally, it is shown that cop win hypergraphs, a generalization of graphs, cannot be characterized in terms of retractions in the same manner as cop win graphs. This thesis presents some small steps towards a solution to Meyniel's Conjecture.

The CC-Game: A Variant Of The Game Of Cops And Robbers

Cops and Robbers is a vertex pursuit game played on graphs. The objective of the game, as the name suggests, is for a set of cops to catch the robber. We study a new variant of this game in which the robber can attack a cop or fight back. This variation restricts the movement of the cops and changes many of the parameters and strategies achieved in the regular game. We explore aspects of this variant such as classifications for certain cop numbers, upper and lower bounds, strategies on special graphs, the cop number on products of graphs, complexity of computations, and density of cops in infinite graphs.

The CC-Game: A Variant Of The Game Of Cops And Robbers

Cops and Robbers is a vertex pursuit game played on graphs. The objective of the game, as the name suggests, is for a set of cops to catch the robber. We study a new variant of this game in which the robber can attack a cop or fight back. This variation restricts the movement of the cops and changes many of the parameters and strategies achieved in the regular game. We explore aspects of this variant such as classifications for certain cop numbers, upper and lower bounds, strategies on special graphs, the cop number on products of graphs, complexity of computations, and density of cops in infinite graphs.

Cops and robbers on graphs and hypergraphs

Cops and Robbers is a vertex-pursuit game played on a graph where a set of cops attempts to capture a robber. Meyniel's Conjecture gives as asymptotic upper bound on the cop number, the number of cops required to win on a connected graph. The incidence graphs of affine planes meet this bound from below, they are called Meyniel extremal. The new parameters mқ and Mқ describe the minimum orders of k-cop-win graphs. The relation of these parameters to Meyniel's Conjecture is discussed. Further, the cop number for all connected graphs of order 10 or less is given. Finally, it is shown that cop win hypergraphs, a generalization of graphs, cannot be characterized in terms of retractions in the same manner as cop win graphs. This thesis presents some small steps towards a solution to Meyniel's Conjecture.

Об одной задаче управляемости и преследования в линейных дискретных системах

In this paper, it is considered linear discrete control and pursuit game problems. Control vectors are subjected to total constraints those are a discrete analogue of the integral constraints. Necessary and sufficient conditions of solvability of the 0-controllability problem are obtained. The connection between 0-controllability and solvability of the pursuit problem is studied. В статье рассмотрена линейные дискретные игровые задачи управления и преследования. На векторы управления накладываются полные ограничения, которые являются дискретным аналогом интегральных ограничений. Получены необходимые и достаточные условия разрешимости проблемы 0-управляемости. Изучается связь между 0-управляемостью и разрешимостью задачи преследования.

Pemanfaatan Modifikasi Permainan Trivial Pursuit Sebagai Media Pembelajaran Guna Meningkatkan Kosakata Bahasa Inggris Anak

The mastery and use of English is very important for social community, especially for children. Children are potential assets in building the nation. Their abilities and intelligence should be optimized to create a developed and competitive nation. Seeing that there is still a lack of elementary shool students in mastering English vocabulary, the researcher were willing to modify the Trivial Pursuit game as learning media to improve children English vocabulary mastery. The Trivial Pursuit game was chosen because this game is very fun when and can unwittingly internalize their knowledge and language. This research was carried out in the historical tourism area of the Banten Lama Kaibon Palace with 10 research subjects and representatives of community elements. This research is qualitative focus on action research where containing the process of planning, making provisions, acting, collecting data, analyzing data, evaluating data, and reflection. The result is proven that there is an improvement in mastery of English vocabulaty after learning by using Trivial Pursuit. The tourisme community also assumed that the action is really helpful to children around tourism site to learn English.