Graph planarity by replacing cliques with paths

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

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


This paper introduces and studies the following beyond-planarity problem, which we call h-CLIQUE2PATH PLANARITY. Let G be a simple topological graph whose vertices are partitioned into subsets of size at most h, each inducing a clique. h-CLIQUE2PATH PLANARITY asks whether it is possible to obtain a planar subgraph of G by removing edges from each clique so that the subgraph induced by each subset is a path. We investigate the complexity of this problem in relation to k-planarity. In particular, 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 when G is a simple 1-plane graph, for any value of h. Our results contribute to the growing fields of hybrid planarity and of graph drawing beyond planarity.

Original languageEnglish (US)
Article number194
Issue number8
StatePublished - Aug 2020


  • Cliques
  • K-planarity
  • NP-hardness
  • Paths
  • Planar graphs
  • Polynomial time reduction

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Numerical Analysis
  • Computational Theory and Mathematics
  • Computational Mathematics


Dive into the research topics of 'Graph planarity by replacing cliques with paths'. Together they form a unique fingerprint.

Cite this