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LexBFS-orderings and powers of graphs

  • Feodor F. Dragan
  • Falk Nicolai
  • Andreas Brandstädt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1197)

Abstract

For an undirected graph G the k-th power G k of G is the graph with the same vertex set as G where two vertices are adjacent iff their distance is at most k in G. In this paper we consider LexBFS-orderings of chordal, distance-hereditaxy and HHD-free graphs (the graphs where each cycle of length at least five has two chords) with respect to their powers. We show that any LexBFS-ordering of a chordal graph is a common perfect elimination ordering of all odd powers of this graph, and any LexBFS-ordering of a distance-hereditary graph is a common perfect elimination ordering of all its even powers. It is wellknown that any LexBFS-ordering of a HHD-free graph is a so-called semi-simplicial ordering. We show, that any LexBFS-ordering of a HHD-free graph is a common semi-simplicial ordering of all its odd powers. Moreover we characterize those chordal, distance-hereditary and HHD-free graphs by forbidden isometric subgraphs for which any LexBFS-ordering of the graph is a common perfect elimination ordering of all its nontrivial powers. As an application we get a linear time approximation of the diameter for weak bipolarizable graphs, a subclass of HHD-free graphs containing all chordal graphs, and an algorithm which computes the diameter and a diametral pair of vertices of a distance-hereditary graph in linear time.

Keywords

Linear Time Steiner Tree Switching Point Interval Graph Chordal Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Feodor F. Dragan
    • 1
  • Falk Nicolai
    • 2
  • Andreas Brandstädt
    • 3
  1. 1.Department of Mathematics and CyberneticsMoldova State UniversityChiŞinĂuMoldova
  2. 2.FB Mathematik, FG InformatikGerhard-Mercator-Universität -GH- DuisburgDuisburgGermany
  3. 3.FB Informatik, Lehrstuhl für Theoretische InformatikUniversität RostockRostockGermany

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