论文标题
图的多机损伤数字
The multi-robber damage number of a graph
论文作者
论文摘要
在图表上的警察和强盗游戏的许多变体中，多个警察对抗一个强盗。 2019年，考克斯（Cox）和萨耶（Sanaei）推出了游戏的一种变体，这使强盗扮演着比简单地逃避警察更积极的角色。在他们的版本中，强盗试图损害尽可能多的顶点，而警察试图最大程度地减少这种损害。虽然最初对损害变体进行了研究，但后来由卡尔森等人扩展到多个警察局。 Al在2021年。我们通过使用多个强盗对一个COP的损害变异来采取不同的方法。具体来说，我们介绍了图的$ S $ - 框架伤害号码，并在此参数上获得各种界限。应用这些边界，我们确定了各种图形系列的$ S $ robber伤害号，并表征具有$ 2 $ 2 $ - 车手损伤号码的图形。
In many variants of the game of Cops and Robbers on graphs, multiple cops play against a single robber. In 2019, Cox and Sanaei introduced a variant of the game that gives the robber a more active role than simply evading the cop. In their version, the robber tries to damage as many vertices as possible and the cop attempts to minimize this damage. While the damage variant was originally studied with one cop and one robber, it was later extended to play with multiple cops by Carlson et. al in 2021. We take a different approach by studying the damage variant with multiple robbers against one cop. Specifically, we introduce the $s$-robber damage number of a graph and obtain a variety of bounds on this parameter. Applying these bounds, we determine the $s$-robber damage number for a variety of graph families and characterize graphs with extreme $2$-robber damage number.
