Contact Representations of Planar Graphs: Extending a Partial Representation is Hard
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10283069" target="_blank" >RIV/00216208:11320/14:10283069 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-319-12340-0_12" target="_blank" >http://dx.doi.org/10.1007/978-3-319-12340-0_12</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-319-12340-0_12" target="_blank" >10.1007/978-3-319-12340-0_12</a>
Alternative languages
Result language
angličtina
Original language name
Contact Representations of Planar Graphs: Extending a Partial Representation is Hard
Original language description
Planar graphs are known to have geometric representations of various types, e.g. as contacts of disks, triangles or - in the bipartite case - vertical and horizontal segments. It is known that such representations can be drawn in linear time, we here wonder whether it is as easy to decide whether a partial representation can be completed to a representation of the whole graph. We show that in each of the cases above, this problem becomes NP-hard. These are the first classes of geometric graphs where extending partial representations is provably harder than recognition, as opposed to e.g. interval graphs, circle graphs, permutation graphs or even standard representations of plane graphs. On the positive side we give two polynomial time algorithms for the grid contact case. The first one is for the case when all vertical segments are pre-represented (note: the problem remains NP-complete when a subset of the vertical segments is specified, even if none of the horizontals are). Secondly,
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)
Others
Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Graph-Theoretic Concepts in Computer Science
ISBN
978-3-319-12339-4
ISSN
0302-9743
e-ISSN
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Number of pages
12
Pages from-to
139-151
Publisher name
Springer Berlin Heidelberg
Place of publication
Neuvedeno
Event location
Nouan-le-Fuzelier
Event date
Jun 25, 2014
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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