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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)

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.

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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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