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(n2)-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.
CITATION STYLE
Li, X., Feng, H., Jiang, H., & Zhu, B. (2016). Polynomial time algorithm for finding a spanning tree with maximum number of internal vertices on interval graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9711, pp. 92–101). Springer Verlag. https://doi.org/10.1007/978-3-319-39817-4_10
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