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Planarity of the 2-Level Cactus Model

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2001

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Dinitz, Yefim
Wagner, Dorothea

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https://doi.org/10.1007/3-540-45477-2_10
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BRANDSTÄDT, Andreas, ed. and others. Graph-Theoretic Concepts in Computer Science : 27th International Workshop, WG 2001, Proceedings. Berlin: Springer, 2001, pp. 91-102. Lecture Notes in Computer Science. 2204. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-3-540-42707-0. Available under: doi: 10.1007/3-540-45477-2_10

Zusammenfassung

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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Graph-Theoretic Concepts in Computer Science : 27th International Workshop, WG 2001, 14. Juni 2001 - 16. Juni 2001, Boltenhagen, Germany
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ISO 690CORNELSEN, Sabine, Yefim DINITZ, Dorothea WAGNER, 2001. Planarity of the 2-Level Cactus Model. Graph-Theoretic Concepts in Computer Science : 27th International Workshop, WG 2001. Boltenhagen, Germany, 14. Juni 2001 - 16. Juni 2001. In: BRANDSTÄDT, Andreas, ed. and others. Graph-Theoretic Concepts in Computer Science : 27th International Workshop, WG 2001, Proceedings. Berlin: Springer, 2001, pp. 91-102. Lecture Notes in Computer Science. 2204. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-3-540-42707-0. Available under: doi: 10.1007/3-540-45477-2_10
BibTex
@inproceedings{Cornelsen2001-10-02Plana-44804,
  year={2001},
  doi={10.1007/3-540-45477-2_10},
  title={Planarity of the 2-Level Cactus Model},
  number={2204},
  isbn={978-3-540-42707-0},
  issn={0302-9743},
  publisher={Springer},
  address={Berlin},
  series={Lecture Notes in Computer Science},
  booktitle={Graph-Theoretic Concepts in Computer Science : 27th International Workshop, WG 2001, Proceedings},
  pages={91--102},
  editor={Brandstädt, Andreas},
  author={Cornelsen, Sabine and Dinitz, Yefim and Wagner, Dorothea}
}
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