TY - JOUR

T1 - Turning cliques into paths to achieve planarity

AU - Angelini, Patrizio

AU - Eades, Peter

AU - Hong, Seok Hee

AU - Klein, Karsten

AU - Kobourov, Stephen

AU - Liotta, Giuseppe

AU - Navarra, Alfredo

AU - Tappini, Alessandra

N1 - Publisher Copyright:
Copyright © 2018, The Authors. All rights reserved.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2018/8/27

Y1 - 2018/8/27

N2 - Motivated by hybrid graph representations, we introduce and study the following beyond-planarity problem, which we call hClique2Path 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.

AB - Motivated by hybrid graph representations, we introduce and study the following beyond-planarity problem, which we call hClique2Path 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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M3 - Article

AN - SCOPUS:85093787865

JO - Nuclear Physics A

JF - Nuclear Physics A

SN - 0375-9474

ER -