Turning Cliques into Paths to Achieve Planarity

  • Patrizio Angelini
  • Peter Eades
  • Seok-Hee Hong
  • Karsten Klein
  • Stephen Kobourov
  • Giuseppe Liotta
  • Alfredo Navarra
  • Alessandra TappiniEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11282)


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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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Patrizio Angelini
    • 1
  • Peter Eades
    • 2
  • Seok-Hee Hong
    • 2
  • Karsten Klein
    • 3
  • Stephen Kobourov
    • 4
  • Giuseppe Liotta
    • 5
  • Alfredo Navarra
    • 5
  • Alessandra Tappini
    • 5
    Email author
  1. 1.University of TübingenTübingenGermany
  2. 2.The University of SydneySydneyAustralia
  3. 3.University of KonstanzKonstanzGermany
  4. 4.University of ArizonaTucsonUSA
  5. 5.University of PerugiaPerugiaItaly

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