Abstract
This paper studies the Maximum Internal Spanning Tree problem which is to find a spanning tree with the maximum number of internal vertices on a graph. We prove that the problem can be solved in polynomial time on interval graphs. The idea is based on the observation that the number of internal vertices in a maximum internal spanning tree is at most one less than the number of edges in a maximum path cover on any graph. On an interval graph, we present an \(O(n^{2})\)-algorithm to find a spanning tree in which the number of internal vertices is exactly one less than the number of edges in a maximum path cover of the graph, where n is the number of vertices in the interval graph.
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This research is supported by the Doctoral Science Foundation of Shanxi Agriculture University under the grant of 2015YJ19.
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Li, X., Feng, H., Jiang, H., Zhu, B. (2016). A Polynomial Time Algorithm for Finding a Spanning Tree with Maximum Number of Internal Vertices on Interval Graphs. In: Zhu, D., Bereg, S. (eds) Frontiers in Algorithmics. FAW 2016. Lecture Notes in Computer Science(), vol 9711. Springer, Cham. https://doi.org/10.1007/978-3-319-39817-4_10
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