保证度量图的Hausdorff-Gromov-Hausdorff等式成立
Guaranteeing Hausdorff-Gromov-Hausdorff Equality for Metric Graphs
AI总结：
该数学研究证明，当度量图与子集的Hausdorff距离满足特定可达条件、且Gromov-Hausdorff距离不超过图收缩率时，二者数值相等。
AI中文摘要：
我们证明，对于度量图G及其子集U⊆G，若G与U间的Hausdorff距离不仅在G的叶节点处达到，且Gromov-Hausdorff距离相对于图的收缩率（systole）不大，则二者满足等式：$d_{GH}(G, U) = d_{H}(G, U)$。
英文摘要：
We prove the equality of Hausdorff and Gromov-Hausdorff distance $d_{GH}(G, U) = d_{H}(G, U)$ for a metric graph $G$ and a subset $U \subseteq G$, given that the Hausdorff distance between $G$ and $U$ is attained not just near the leaves of $G$ and the Gromov-Hausdorff distance is not too big compared to the graph's systole.
