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Planarity of the 2-Level Cactus Model

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Graph-Theoretic Concepts in Computer Science (WG 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2204))

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Abstract

The 2-level cactus introduced by Dinitz and Nutov in [5] is a data structure that represents the minimum and minimum+1 edgecuts of an undirected connected multi-graph G in a compact way. In this paper, we study planarity of the 2-level cactus, which can be used, e.g., in graph drawing. We give a new sufficient planarity criterion in terms of projection paths over a spanning subtree of a graph. Using this criterion, we show that the 2-level cactus of G is planar if the cardinality of a minimum edge-cut of G is not equal to 2, 3 or 5. On the other hand, we give examples for non-planar 2-level cacti of graphs with these connectivities.

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Author information

Authors and Affiliations

  1. Dept. of Computer and Information Science, University of Konstanz, Germany

    Sabine Cornelsen & Dorothea Wagner

  2. Dept. of Computer Science, Ben-Gurion University, Israel

    Yefim Dinitz

Authors
  1. Sabine Cornelsen
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  2. Yefim Dinitz
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  3. Dorothea Wagner
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Rostock, 18051, Rostock, Germany

    Andreas Brandstädt  & Van Bang Le  & 

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© 2001 Springer-Verlag Berlin Heidelberg

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Cornelsen, S., Dinitz, Y., Wagner, D. (2001). Planarity of the 2-Level Cactus Model. In: Brandstädt, A., Le, V.B. (eds) Graph-Theoretic Concepts in Computer Science. WG 2001. Lecture Notes in Computer Science, vol 2204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45477-2_10

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  • DOI: https://doi.org/10.1007/3-540-45477-2_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42707-0

  • Online ISBN: 978-3-540-45477-9

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