Turning cliques into paths to achieve planarity

Patrizio Angelini, Peter Eades, Seok Hee Hong, Karsten Klein, Stephen G Kobourov, Giuseppe Liotta, Alfredo Navarra, Alessandra Tappini

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish (US)
Title of host publicationGraph Drawing and Network Visualization - 26th International Symposium, GD 2018, Proceedings
EditorsTherese Biedl, Andreas Kerren
PublisherSpringer-Verlag
Pages67-74
Number of pages8
ISBN (Print)9783030044138
DOIs
StatePublished - Jan 1 2018
Event26th International Symposium on Graph Drawing and Network Visualization, GD 2018 - Barcelona, Spain
Duration: Sep 26 2018Sep 28 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11282 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other26th International Symposium on Graph Drawing and Network Visualization, GD 2018
CountrySpain
CityBarcelona
Period9/26/189/28/18

Fingerprint

Planarity
Clique
Path
Topological Graph
Subset
Plane Graph
Graph Representation
Induced Subgraph
Simple Graph
Linear Time
Subgraph
NP-complete problem
Graph in graph theory

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Angelini, P., Eades, P., Hong, S. H., Klein, K., Kobourov, S. G., Liotta, G., ... Tappini, A. (2018). Turning cliques into paths to achieve planarity. In T. Biedl, & A. Kerren (Eds.), 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.

Graph Drawing and Network Visualization - 26th International Symposium, GD 2018, Proceedings. ed. / Therese Biedl; Andreas Kerren. Springer-Verlag, 2018. p. 67-74 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11282 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Angelini, P, Eades, P, Hong, SH, Klein, K, Kobourov, SG, Liotta, G, Navarra, A & Tappini, A 2018, Turning cliques into paths to achieve planarity. in T Biedl & A Kerren (eds), 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
Angelini P, Eades P, Hong SH, Klein K, Kobourov SG, Liotta G et al. Turning cliques into paths to achieve planarity. In Biedl T, Kerren A, editors, Graph Drawing and Network Visualization - 26th International Symposium, GD 2018, Proceedings. Springer-Verlag. 2018. p. 67-74. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-030-04414-5_5
Angelini, Patrizio ; Eades, Peter ; Hong, Seok Hee ; Klein, Karsten ; Kobourov, Stephen G ; Liotta, Giuseppe ; Navarra, Alfredo ; Tappini, Alessandra. / Turning cliques into paths to achieve planarity. Graph Drawing and Network Visualization - 26th International Symposium, GD 2018, Proceedings. editor / Therese Biedl ; Andreas Kerren. Springer-Verlag, 2018. pp. 67-74 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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