Graph connectivity and its augmentation: applications of MA orderings

Authors:
Hiroshi Nagamochi;Toshihide Ibaraki
Affiliations:
Department of Information and Computer Sciences, Toyohashi University of Technology, Hibarigaoka, Tenpaku, Toyohashi 441-8580, Japan;Department of Applied Mathematics and Physics, Kyoto University, Sakyo, Kyoto 606-8501, Japan
Venue:
Discrete Applied Mathematics
Year:
2002

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Abstract

This paper surveys how the maximum adjacency (MA) ordering of the vertices in a graph can be used to solve various graph problems. We first explain that the minimum cut problem can be solved efficiently by utilizing the MA ordering. The idea is then extended to a fundamental operation of a graph, edge splitting. Based on this, the edge-connectivity augmentation problem for a given k (and also for the entire range of k) can be solved efficiently by making use of the MA ordering, where it is asked to add the smallest number of new edges to a given graph so that its edge-connectivity is increased to k. Other related topics are also surveyed.