Geodesic
Clustered planarity testing revisited
The electronic journal of combinatorics, Tome 22 (2015) no. 4
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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 with 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.
DOI : 10.37236/5002
Classification : 05C10, 68R10, 15A06, 05B35
Mots-clés : graph planarity, clustered planarity, Hanani-Tutte theorem, matroid intersection algorithm 
@article{10_37236_5002,
     author = {Radoslav Fulek and Jan Kyn\v{c}l and Igor Malinovi\'c and D\"om\"ot\"or P\'alv\"olgyi},
     title = {Clustered planarity testing revisited},
     journal = {The electronic journal of combinatorics},
     year = {2015},
     volume = {22},
     number = {4},
     doi = {10.37236/5002},
     zbl = {1327.05076},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/5002/}
}
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Radoslav Fulek; Jan Kynčl; Igor Malinović; Dömötör Pálvölgyi. Clustered planarity testing revisited. The electronic journal of combinatorics, Tome 22 (2015) no. 4. doi: 10.37236/5002

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