In this paper, we study the Maximum Internal Spanning Tree Problem (MIST). Given an undirected simple graph G, the task for the Maximum Internal Spanning Tree problem is to find a spanning tree of G with maximum number of internal vertices. We present an approximation algorithm with performance ratio $\frac{4}{3}$, which improves upon the best known performance ratio $\frac{3}{2}$. Our algorithm benefits from a new observation for bounding the number of internal vertices of a spanning tree. We can also give an example to show that the performance ratio $\frac{4}{3}$ is actually tight for this algorithm. Finally, we show that MIST is Max-SNP-hard.

中文翻译：

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一种 $\frac{4}{3}$内部生成树问题的最大近似算法

在本文中，我们研究了最大内部生成树问题（MIST）。给定一个无向的简单图G，最大内部生成树问题的任务是找到具有最大内部顶点数量的G的生成树。我们提出一种具有性能比的近似算法$\frac{4}{3}$，从而改善了最知名的性能比 $\frac{3}{2}$。我们的算法得益于对生成树内部顶点数量进行限制的新观察。我们还可以举一个例子来说明性能比$\frac{4}{3}$实际上对于该算法来说是严格的。最后，我们证明MIST是Max-SNP困难的。