Turning Cliques into Paths to Achieve Planarity release_qgpm7w5lvvdgldue3opaplqxca

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

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2018  

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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Date   2018-08-27
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arXiv  1808.08925v1
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