### Abstract

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.

Original language | English (US) |
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Title of host publication | Graph Drawing and Network Visualization - 26th International Symposium, GD 2018, Proceedings |

Editors | Therese Biedl, Andreas Kerren |

Publisher | Springer-Verlag |

Pages | 67-74 |

Number of pages | 8 |

ISBN (Print) | 9783030044138 |

DOIs | |

State | Published - Jan 1 2018 |

Event | 26th International Symposium on Graph Drawing and Network Visualization, GD 2018 - Barcelona, Spain Duration: Sep 26 2018 → Sep 28 2018 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11282 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 26th International Symposium on Graph Drawing and Network Visualization, GD 2018 |
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Country | Spain |

City | Barcelona |

Period | 9/26/18 → 9/28/18 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Graph Drawing and Network Visualization - 26th International Symposium, GD 2018, Proceedings*(pp. 67-74). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11282 LNCS). Springer-Verlag. https://doi.org/10.1007/978-3-030-04414-5_5

**Turning cliques into paths to achieve planarity.** / Angelini, Patrizio; Eades, Peter; Hong, Seok Hee; Klein, Karsten; Kobourov, Stephen G; Liotta, Giuseppe; Navarra, Alfredo; Tappini, Alessandra.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Graph Drawing and Network Visualization - 26th International Symposium, GD 2018, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11282 LNCS, Springer-Verlag, pp. 67-74, 26th International Symposium on Graph Drawing and Network Visualization, GD 2018, Barcelona, Spain, 9/26/18. https://doi.org/10.1007/978-3-030-04414-5_5

}

TY - GEN

T1 - Turning cliques into paths to achieve planarity

AU - Angelini, Patrizio

AU - Eades, Peter

AU - Hong, Seok Hee

AU - Klein, Karsten

AU - Kobourov, Stephen G

AU - Liotta, Giuseppe

AU - Navarra, Alfredo

AU - Tappini, Alessandra

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85059092003&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85059092003&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-04414-5_5

DO - 10.1007/978-3-030-04414-5_5

M3 - Conference contribution

AN - SCOPUS:85059092003

SN - 9783030044138

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 67

EP - 74

BT - Graph Drawing and Network Visualization - 26th International Symposium, GD 2018, Proceedings

A2 - Biedl, Therese

A2 - Kerren, Andreas

PB - Springer-Verlag

ER -