图中边测集的一种算法
An Algorithm for Monitoring Edge-geodetic Sets in Chordal Graphs
AI总结：
本文研究了弦图中边测集的最小生成问题，证明弦图具有唯一的最小边测集，解决了Foucaud等人提出的开放性问题。
摘要：
一个监控边测集（或简称meg-set）是一个顶点集合M，使得当任意边被移除时，M中某些顶点之间的距离会增加。这一概念由Foucaud等人于2023年引入，作为监控通信故障的网络方法。由于一般情况下计算最小meg-set是困难的，最近的研究致力于在受限图类中寻找多项式时间算法来计算最小meg-set。大多数结果基于某些图类具有唯一最小meg-set的性质，从而易于计算。在本文中，我们证明弦图也具有唯一的最小meg-set，回答了Foucaud等人提出的开放性问题。
英文摘要：
A monitoring edge-geodetic set (or meg-set for short) of a graph is a set of vertices $M$ such that if any edge is removed, then the distance between some two vertices of $M$ increases. This notion was introduced by Foucaud et al. in 2023 as a way to monitor networks for communication failures. As computing a minimum meg-set is hard in general, recent works aimed to find polynomial-time algorithms to compute minimum meg-sets when the input belongs to a restricted class of graphs. Most of these results are based on the property of some classes of graphs to admit a unique minimal meg-set, which is then easy to compute. In this work, we prove that chordal graphs also admit a unique minimal meg-set, answering a standing open question of Foucaud et al.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
