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%2F13%3A10135346" target="_blank" >RIV/00216208:11320/13:10135346 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.comgeo.2012.07.005" target="_blank" >http://dx.doi.org/10.1016/j.comgeo.2012.07.005</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.comgeo.2012.07.005" target="_blank" >10.1016/j.comgeo.2012.07.005</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, H), where G is a graph, H is a subgraph of G, and H is a planar embedding of H. We say that a PEG (G, H, H) is planar if the graph G has a planar embedding that extends the embedding H. 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 an obstruction.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GEGIG%2F11%2FE023" target="_blank" >GEGIG/11/E023: Graph Drawings and Representations</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Computational Geometry: Theory and Applications
ISSN
0925-7721
e-ISSN
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Volume of the periodical
46
Issue of the periodical within the volume
4
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
27
Pages from-to
466-492
UT code for WoS article
000314437000006
EID of the result in the Scopus database
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