Minimum Vertex Ranking Spanning Tree Problem on Some Classes of Graphs

Authors:
Ruei-Yuan Chang;Guanling Lee;Sheng-Lung Peng
Affiliations:
Department of Computer Science and Information Engineering, National Dong Hwa University, Hualien, Taiwan 974;Department of Computer Science and Information Engineering, National Dong Hwa University, Hualien, Taiwan 974;Department of Computer Science and Information Engineering, National Dong Hwa University, Hualien, Taiwan 974
Venue:
ICIC '08 Proceedings of the 4th international conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications - with Aspects of Artificial Intelligence
Year:
2008

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Abstract

A vertex ranking of a graph Gis a labeling of the vertices of Gwith positive integers such that every path between two vertices with the same label icontains 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 Gis to find a spanning tree Tof Gsuch that the minimum vertex ranking of Tis 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(n3) time on interval graphs where nis the number of vertices in the input graph.