MSTCI问题的三个方面
Three aspects of the MSTCI problem
AI总结：
本文研究MSTCI问题，即寻找生成树以最小化环交集数量，在一般连通图中给出了交集数的两个下界，比较了相差一条边的图的交集数，并尝试推广关于万能顶点图的近期结果。
摘要：
考虑一个连通图$G$，设$T$是$G$的一棵生成树。$G-T$中的每条边$e$在$T \cup \{e\}$中诱导一个环。两个不同这样的环的交集是$T$中同时属于这两个环的边的集合。MSTCI问题在于寻找一棵生成树，使得这种非空交集的数量最少，交集数是指一个解中非空交集的数量。在本文中，我们在一般背景下（即对于任意连通图）考虑该问题的三个方面。第一方面给出了交集数的两个下界。第二方面比较了仅相差一条边的图的交集数。最后一方面尝试推广一个关于具有万能顶点的图的近期结果。
英文摘要：
Consider a connected graph $G$ and let $T$ be a spanning tree of $G$. Every edge $e \in G-T$ induces a cycle in $T \cup \{e\}$. The intersection of two distinct such cycles is the set of edges of $T$ that belong to both cycles. The MSTCI problem consists in finding a spanning tree that has the least number of such non-empty intersections and the instersection number is the number of non-empty intersections of a solution. In this article we consider three aspects of the problem in a general context (i.e. for arbitrary connected graphs). The first presents two lower bounds of the intersection number. The second compares the intersection number of graphs that differ in one edge. The last is an attempt to generalize a recent result for graphs with a universal vertex.
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。
