Clustered planarity testing revisited

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10282839" target="_blank" >RIV/00216208:11320/14:10282839 - isvavai.cz</a>
Result on the web
<a href="http://link.springer.com/content/pdf/10.1007%2F978-3-662-45803-7_36.pdf" target="_blank" >http://link.springer.com/content/pdf/10.1007%2F978-3-662-45803-7_36.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-662-45803-7_36" target="_blank" >10.1007/978-3-662-45803-7_36</a>

Result language
angličtina
Original language name
Clustered planarity testing revisited
Original language description
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.
Czech name
—
Czech description
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Project
<a href="/en/project/GEGIG%2F11%2FE023" target="_blank" >GEGIG/11/E023: Graph Drawings and Representations</a><br>
Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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