图及其细分上的入侵者搜索
Searching for an Intruder on Graphs and Their Subdivisions
摘要：
在本文中，我们分析了一个变种的追逃对策游戏图$G$的入侵者占据一个顶点，被允许移动到邻顶点或留在原地，是“看不见的”，这意味着，在没有知识的入侵者的位置的情况下操作。在每个阶段，允许检查员检查任意一组$k$顶点。最小的$k$，对于它的入侵者可以保证捕获被称为检查数的$G$。我们还介绍和研究拓扑检查数，一个数量，捕捉下的细分$G$的检查数的限制行为。我们的中心定理提供了一个完整的分类图的拓扑检查数高达$3$。
英文摘要：
In this paper we analyze a variant of the pursuit-evasion game on a graph $G$ where the intruder occupies a vertex, is allowed to move to adjacent vertices or remain in place, and is 'invisible' to the searcher, meaning that the searcher operates with no knowledge of the position of the intruder. On each stage, the searcher is allowed to inspect an arbitrary set of $k$ vertices. The minimum $k$ for which the searcher can guarantee the capture of the intruder is called the inspection number of $G$. We also introduce and study the topological inspection number, a quantity that captures the limiting behavior of the inspection number under subdivisions of $G$. Our central theorem provides a full classification of graphs with topological inspection number up to $3$.
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