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Ambush Cops and Robbers
Graphs and Combinatorics ( IF 0.7 ) Pub Date : 2021-10-28 , DOI: 10.1007/s00373-021-02395-6
Nancy E. Clarke 1 , Melissa Creighton 1 , Patrick Murray 1 , Asiyeh Sanaei 2
Affiliation  

A variation of the Cops and Robber game is introduced in which the robber side consists of two robbers. The cops win by moving onto the same vertex as one of the robbers after a finite number of moves. As in the original game, the robber side can win by avoiding capture indefinitely. In this version, however, the robbers can also win by both moving onto the same vertex as the cop at the same time. Otherwise, the robbers must be located on distinct vertices. We present structural properties of ambush-copwin graphs, those graphs on which a single cop can guarantee a win. As well, we characterize ambush-copwin graphs of girth \(g \ge 4\) and classes of ambush-copwin graphs of girth 3, particularly a class of chordal graphs.



中文翻译:

伏击警察和强盗

引入了警察和强盗游戏的变体,其中强盗方由两个强盗组成。在有限次数的移动后,警察通过移动到与劫匪之一相同的顶点来获胜。与原始游戏一样,强盗方可以通过无限期地避免捕获来获胜。然而,在这个版本中,强盗也可以通过同时移动到与警察相同的顶点来获胜。否则,劫匪必须位于不同的顶点上。我们展示了 ambush-copwin 图的结构特性,在这些图上单个警察可以保证获胜。同样,我们描述了围长\(g \ge 4\)的埋伏-copwin 图和围长 3 的埋伏-copwin 图的类,特别是一类弦图。

更新日期:2021-10-28
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