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

4 Scopus citations

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Angelini, P., Eades, P., Hong, S. H., Klein, K., Kobourov, S. G., 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 (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