A Kuratowski-type theorem for planarity of partially embedded graphs
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F11%3A10100586" target="_blank" >RIV/00216208:11320/11:10100586 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1145/1998196.1998214" target="_blank" >http://dx.doi.org/10.1145/1998196.1998214</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1145/1998196.1998214" target="_blank" >10.1145/1998196.1998214</a>
Alternative languages
Result language
angličtina
Original language name
A Kuratowski-type theorem for planarity of partially embedded graphs
Original language description
A partially embedded graph (or PEG) is a triple (G,H,EH), where G is a graph, H is a subgraph of G, and EH is a planar embedding of H. We say that a PEG (G,H,EH) is planar if the graph G has a planar embedding that extends the embedding EH. We introducea containment relation of PEGs analogous to graph minor containment, and characterize the minimal non-planar PEGs with respect to this relation. We show that all the minimal non-planar PEGs except for finitely many belong to a single easily recognizableand explicitly described infinite family. We also describe a more complicated containment relation which only has a finite number of minimal non-planar PEGs. Furthermore, by extending an existing planarity test for PEGs, we obtain a polynomial-time algorithm which, for a given PEG, either produces a planar embedding or identifies a minimal obstruction.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
IN - Informatics
OECD FORD branch
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Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Proceedings of the 27th annual ACM symposium on Computational geometry
ISBN
978-1-4503-0682-9
ISSN
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e-ISSN
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Number of pages
10
Pages from-to
107-116
Publisher name
ACM
Place of publication
New York
Event location
Paříž, Francie
Event date
Jun 13, 2011
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000292906900013