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Homogeneously orderable graphs and the Steiner tree problem

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Graph-Theoretic Concepts in Computer Science (WG 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1017))

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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.

Second author supported by the VW-Stiftung Project No. I/69041 and by DAAD

Third author supported by DFG

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References

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Author information

Authors and Affiliations

  1. Fachbereich Informatik, Lehrstuhl für Theoretische Informatik, Universität Rostock, D 18051, Rostock, Germany

    Andreas Brandstädt

  2. Department of Mathematics and Cybernetics Moldova State University, A. Mateevici str. 60, 277009, ChiŞ.inĂu, Moldova

    Feodor F. Dragan

  3. Gerhard-Mercator-Universität -GH-Duisburg FB Mathematik FG Informatik I, D 47048, Duisburg, Germany

    Falk Nicolai

Authors
  1. Andreas Brandstädt
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  2. Feodor F. Dragan
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  3. Falk Nicolai
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Manfred Nagl

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© 1995 Springer-Verlag Berlin Heidelberg

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Brandstädt, A., Dragan, F.F., Nicolai, F. (1995). Homogeneously orderable graphs and the Steiner tree problem. In: Nagl, M. (eds) Graph-Theoretic Concepts in Computer Science. WG 1995. Lecture Notes in Computer Science, vol 1017. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60618-1_90

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  • DOI: https://doi.org/10.1007/3-540-60618-1_90

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60618-5

  • Online ISBN: 978-3-540-48487-5

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