Abstract
This paper focuses on finding a spanning tree of a graph to maximize its internal vertices in number. We propose a new upper bound for the number of internal vertices in a spanning tree, which shows that for any undirected simple graph, any spanning tree has less internal vertices than the edges a maximum path-cycle cover has. Thus starting with a maximum path-cycle cover, we can devise an approximation algorithm with a performance ratio \(\frac{3}{2}\) for this problem on undirected simple graphs. This improves upon the best known performance ratio \(\frac{5}{3}\) achieved by the algorithm of Knauer and Spoerhase. Furthermore, we can improve the algorithm to achieve a performance ratio \(\frac{4}{3}\) for this problem on graphs without leaves.
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Li, X., Zhu, D. (2014). Approximating the Maximum Internal Spanning Tree Problem via a Maximum Path-Cycle Cover. In: Ahn, HK., Shin, CS. (eds) Algorithms and Computation. ISAAC 2014. Lecture Notes in Computer Science(), vol 8889. Springer, Cham. https://doi.org/10.1007/978-3-319-13075-0_37
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DOI: https://doi.org/10.1007/978-3-319-13075-0_37
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