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Homogeneously orderable graphs and the Steiner tree problem

  • Andreas Brandstädt
  • Feodor F. Dragan
  • Falk Nicolai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1017)

Abstract

In this paper we introduce homogeneously orderable graphs which are a common generalization of distance-hereditary graphs, dually chordal graphs and homogeneous graphs. We present a characterization of the new class in terms of a tree structure of the closed neighbourhoods of homogeneous sets in 2-graphs which is closely related to the defining elimination ordering.

The local structure of homogeneously orderable graphs implies a simple polynomial time recognition algorithm for these graphs. Finally we give a polynomial time solution for the Steiner tree problem on homogeneously orderable graphs which extends the efficient solutions of that problem on distance-hereditary graphs, dually chordal graphs and homogeneous graphs.

Keywords

Maximal Clique Chordal Graph Graph Class Steiner Tree Problem Orderable 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 1995

Authors and Affiliations

  • Andreas Brandstädt
    • 1
  • Feodor F. Dragan
    • 2
  • Falk Nicolai
    • 3
  1. 1.Fachbereich Informatik, Lehrstuhl für Theoretische InformatikUniversität RostockRostockGermany
  2. 2.Department of Mathematics and Cybernetics Moldova State UniversityChiŞ.inĂuMoldova
  3. 3.Gerhard-Mercator-Universität -GH-Duisburg FB Mathematik FG Informatik IDuisburgGermany

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