Abstract
A vertex ranking of a graph G is a labeling of the vertices of G with positive integers such that every path between two vertices with the same label i contains a vertex with label j > i. A vertex ranking is minimum if the largest label used in it is the smallest among all possible vertex rankings of G. The minimum vertex ranking spanning tree problem on G is to find a spanning tree T of G such that the minimum vertex ranking of T is minimum among all possible spanning trees of G. In this paper, we show that the minimum vertex ranking spanning tree problem on interval graphs, split graphs, and cographs can be solved in linear time. It improves a previous result that runs in O(n 3) time on interval graphs where n is the number of vertices in the input graph.
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Chang, RY., Lee, G., Peng, SL. (2008). Minimum Vertex Ranking Spanning Tree Problem on Some Classes of Graphs. In: Huang, DS., Wunsch, D.C., Levine, D.S., Jo, KH. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence. ICIC 2008. Lecture Notes in Computer Science(), vol 5227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85984-0_91
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DOI: https://doi.org/10.1007/978-3-540-85984-0_91
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85983-3
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