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Completely Connected Clustered Graphs

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2003

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Wagner, Dorothea

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https://doi.org/10.1007/978-3-540-39890-5_15
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BODLAENDER, Hans L., ed.. Graph-Theoretic Concepts in Computer Science : 29th International Workshop, WG 2003, Revised Papers. Berlin: Springer, 2003, pp. 168-179. Lecture Notes in Computer Science. 2880. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-3-540-20452-7. Available under: doi: 10.1007/978-3-540-39890-5_15

Zusammenfassung

Planar drawings of clustered graphs are considered. We introduce the notion of completely connected clustered graphs, i.e. hierarchically clustered graphs that have the property that not only every cluster but also each complement of a cluster induces a connected subgraph. As a main result, we prove that a completely connected clustered graph is c-planar if and only if the underlying graph is planar. Further, we investigate the influence of the root of the inclusion tree to the choice of the outer face of the underlying graph and vice versa.

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Graph-Theoretic Concepts in Computer Science : 29th International Workshop, WG 2003, 19. Juni 2003 - 21. Juni 2003, Elspeet, The Netherlands
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ISO 690CORNELSEN, Sabine, Dorothea WAGNER, 2003. Completely Connected Clustered Graphs. Graph-Theoretic Concepts in Computer Science : 29th International Workshop, WG 2003. Elspeet, The Netherlands, 19. Juni 2003 - 21. Juni 2003. In: BODLAENDER, Hans L., ed.. Graph-Theoretic Concepts in Computer Science : 29th International Workshop, WG 2003, Revised Papers. Berlin: Springer, 2003, pp. 168-179. Lecture Notes in Computer Science. 2880. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-3-540-20452-7. Available under: doi: 10.1007/978-3-540-39890-5_15
BibTex
@inproceedings{Cornelsen2003Compl-44801,
  year={2003},
  doi={10.1007/978-3-540-39890-5_15},
  title={Completely Connected Clustered Graphs},
  number={2880},
  isbn={978-3-540-20452-7},
  issn={0302-9743},
  publisher={Springer},
  address={Berlin},
  series={Lecture Notes in Computer Science},
  booktitle={Graph-Theoretic Concepts in Computer Science : 29th International Workshop, WG 2003, Revised Papers},
  pages={168--179},
  editor={Bodlaender, Hans L.},
  author={Cornelsen, Sabine and Wagner, Dorothea}
}
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