Clustered planarity testing revisited Journal Article


Author(s): Fulek, Radoslav; Kynčl, Jan; Malinovič, Igor; Pálvölgyi, Dömötör
Article Title: Clustered planarity testing revisited
Affiliation IST Austria
Abstract: The Hanani-Tutte theorem is a classical result proved for the first time in the 1930s that characterizes planar graphs as graphs that admit a drawing in the plane in which every pair of edges not sharing a vertex cross an even number of times. We generalize this result to clustered graphs with two disjoint clusters, and show that a straightforward extension to flat clustered graphs with three or more disjoint clusters is not possible. For general clustered graphs we show a variant of the Hanani-Tutte theorem in the case when each cluster induces a connected subgraph. Di Battista and Frati proved that clustered planarity of embedded clustered graphs whose every face is incident to at most five vertices can be tested in polynomial time. We give a new and short proof of this result, using the matroid intersection algorithm.
Keywords: Clustered planarity; Graph planarity; Hanani-Tutte theorem; Matroid intersection algorithm
Journal Title: Electronic Journal of Combinatorics
Volume: 22
Issue 4
ISSN: 1097-1440
Publisher: Electronic Journal of Combinatorics  
Date Published: 2015-11-13
Start Page: Article number: P4.24
URL:
Notes: The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no [291734], and ESF Eurogiga project GraDR as GA CR GIG/11/E023.
Open access: yes (OA journal)
IST Austria Authors
  1. Radoslav Fulek
    14 Fulek
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