We give an improved lower bound of 10/3 on the competitive ratio for the exploration of an undirected, edge-weighted graph with a single agent that needs to return to the starting location after visiting all vertices. We assume that the agent has full knowledge of all edges incident to visited vertices, and, in particular, vertices have unique identifiers. Our bound improves a lower bound of 2.5 by Dobrev et al. [10] and also holds for planar graphs, where it complements an upper bound of 16 by Megow et al. [20]. The question whether a constant competitive ratio can be achieved in general remains open.

中文翻译：

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竞争图探索的改进下限

对于使用单个代理的无向边加权图的探索，我们需要将竞争比的下限改进为10/3，在访问所有顶点后需要返回到起始位置。我们假定代理对入射到访问的顶点的所有边都具有完全的了解，尤其是顶点具有唯一的标识符。Dobrev等人将界线提高了2.5的下界。[10]也适用于平面图，它补充了Megow等人的上限16。[20]。总的来说，能否实现恒定的竞争比率尚待解决。