Minimum edge ranking spanning trees of split graphs

Authors:
Kazuhisa Makino;Yushi Uno;Toshihide Ibaraki
Affiliations:
Department of Mathematical Informatics, Graduate School of Information and Technology, University of Tokyo, Tokyo, Japan;Department of Mathematics and Information Sciences, Graduate School of Science, Osaka Prefecture University, Sakai, Japan;Department of Informatics, School of Science and Technology, Kwansei Gakuin University, Sanda, Japan
Venue:
Discrete Applied Mathematics - Special issue: Discrete algorithms and optimization, in honor of professor Toshihide Ibaraki at his retirement from Kyoto University
Year:
2006

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Abstract

Given a graph G, the minimum edge ranking spanning tree problem (MERST) is to find a spanning tree of G whose edge ranking is minimum. However, this problem is known to be NP-hard for general graphs. In this paper, we show that the problem MERST has a polynomial time algorithm for split graphs, which have useful applications in practice. The result is also significant in the sense that this is a first non-trivial graph class for which the problem MERST is found to be polynomially solvable. We also show that the problem MERST for threshold graphs can be solved in linear time, where threshold graphs are known to be split.