Turning Cliques into Paths to Achieve Planarity

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2018
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Angelini, Patrizio
Eades, Peter
Hong, Seok-Hee
Kobourov, Stephen
Liotta, Giuseppe
Navarra, Alfredo
Tappini, Alessandra
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BIEDL, Therese, ed., Andreas KERREN, ed.. Graph Drawing and Network Visualization : 26th International Symposium, GD 2018, Barcelona, Spain, September 26-28, 2018, proceedings. Cham: Springer, 2018, pp. 67-74. Lecture Notes in Computer Science. 11282. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-3-030-04413-8. Available under: doi: 10.1007/978-3-030-04414-5_5
Zusammenfassung

Motivated by hybrid graph representations, we introduce and study the following beyond-planarity problem, which we call h -Clique2Path Planarity: Given a graph G, whose vertices are partitioned into subsets of size at most h, each inducing a clique, remove edges from each clique so that the subgraph induced by each subset is a path, in such a way that the resulting subgraph of G is planar. We study this problem when G is a simple topological graph, and establish its complexity in relation to k-planarity. We prove that h -Clique2Path Planarity is NP-complete even when h=4 and G is a simple 3-plane graph, while it can be solved in linear time, for any h, when G is 1-plane

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26th International Symposium, GD 2018, 26. Sept. 2018 - 28. Sept. 2018, Barcelona, Spain
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ISO 690ANGELINI, Patrizio, Peter EADES, Seok-Hee HONG, Karsten KLEIN, Stephen KOBOUROV, Giuseppe LIOTTA, Alfredo NAVARRA, Alessandra TAPPINI, 2018. Turning Cliques into Paths to Achieve Planarity. 26th International Symposium, GD 2018. Barcelona, Spain, 26. Sept. 2018 - 28. Sept. 2018. In: BIEDL, Therese, ed., Andreas KERREN, ed.. Graph Drawing and Network Visualization : 26th International Symposium, GD 2018, Barcelona, Spain, September 26-28, 2018, proceedings. Cham: Springer, 2018, pp. 67-74. Lecture Notes in Computer Science. 11282. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-3-030-04413-8. Available under: doi: 10.1007/978-3-030-04414-5_5
BibTex
@inproceedings{Angelini2018-12-18Turni-44694,
  year={2018},
  doi={10.1007/978-3-030-04414-5_5},
  title={Turning Cliques into Paths to Achieve Planarity},
  number={11282},
  isbn={978-3-030-04413-8},
  issn={0302-9743},
  publisher={Springer},
  address={Cham},
  series={Lecture Notes in Computer Science},
  booktitle={Graph Drawing and Network Visualization : 26th International Symposium, GD 2018, Barcelona, Spain, September 26-28, 2018, proceedings},
  pages={67--74},
  editor={Biedl, Therese and Kerren, Andreas},
  author={Angelini, Patrizio and Eades, Peter and Hong, Seok-Hee and Klein, Karsten and Kobourov, Stephen and Liotta, Giuseppe and Navarra, Alfredo and Tappini, Alessandra}
}
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