Clustered planarity testing revisited

R. Fulek, J. Kynčl, I. Malinovič, D. Pálvölgyi, Electronic Journal of Combinatorics 22 (2015).

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Journal Article | Published | English
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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.
Publishing Year
Date Published
2015-11-13
Journal Title
Electronic Journal of Combinatorics
Volume
22
Issue
4
Article Number
P4.24
IST-REx-ID

Cite this

Fulek R, Kynčl J, Malinovič I, Pálvölgyi D. Clustered planarity testing revisited. Electronic Journal of Combinatorics. 2015;22(4).
Fulek, R., Kynčl, J., Malinovič, I., & Pálvölgyi, D. (2015). Clustered planarity testing revisited. Electronic Journal of Combinatorics, 22(4).
Fulek, Radoslav, Jan Kynčl, Igor Malinovič, and Dömötör Pálvölgyi. “Clustered Planarity Testing Revisited.” Electronic Journal of Combinatorics 22, no. 4 (2015).
R. Fulek, J. Kynčl, I. Malinovič, and D. Pálvölgyi, “Clustered planarity testing revisited,” Electronic Journal of Combinatorics, vol. 22, no. 4, 2015.
Fulek R, Kynčl J, Malinovič I, Pálvölgyi D. 2015. Clustered planarity testing revisited. Electronic Journal of Combinatorics. 22(4).
Fulek, Radoslav, et al. “Clustered Planarity Testing Revisited.” Electronic Journal of Combinatorics, vol. 22, no. 4, P4.24, Electronic Journal of Combinatorics, 2015.
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