On the Complexity of Planar Covering of Small Graphs
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F11%3A10125858" target="_blank" >RIV/00216208:11320/11:10125858 - isvavai.cz</a>
Result on the web
<a href="http://link.springer.com/chapter/10.1007%2F978-3-642-25870-1_9?LI=true" target="_blank" >http://link.springer.com/chapter/10.1007%2F978-3-642-25870-1_9?LI=true</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-642-25870-1_9" target="_blank" >10.1007/978-3-642-25870-1_9</a>
Alternative languages
Result language
angličtina
Original language name
On the Complexity of Planar Covering of Small Graphs
Original language description
The problem Cover(H) asks whether an input graph G covers a fixed graph H (i.e., whether there exists a homomorphism G to H which locally preserves the structure of the graphs). Complexity of this problem has been intensively studied. In this paper, we consider the problem PlanarCover(H) which restricts the input graph G to be planar. PlanarCover(H) is polynomially solvable if Cover(H) belongs to P, and it is even trivially solvable if H has no planar cover. Thus the interesting cases are when H admitsa planar cover, but Cover(H) is NP-complete. This also relates the problem to the long-standing Negami Conjecture which aims to describe all graphs having a planar cover. Kratochvil asked whether there are non-trivial graphs for which Cover(H) is NP-complete but PlanarCover(H) belongs to P. We examine the first nontrivial cases of graphs H for which Cover(H) is NP-complete and which admit a planar cover. We prove NP-completeness of PlanarCover(H) in these cases.
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>S - Specificky vyzkum na vysokych skolach
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
Lecture Notes in Computer Science
ISBN
978-3-642-25869-5
ISSN
0302-9743
e-ISSN
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Number of pages
12
Pages from-to
83-94
Publisher name
Springer
Place of publication
Berlin Heidelberg
Event location
Teplá
Event date
Jun 21, 2011
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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