Planar Graphs as VPG-Graphs
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10190904" target="_blank" >RIV/00216208:11320/13:10190904 - isvavai.cz</a>
Result on the web
<a href="http://link.springer.com/chapter/10.1007/978-3-642-36763-2_16" target="_blank" >http://link.springer.com/chapter/10.1007/978-3-642-36763-2_16</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-642-36763-2_16" target="_blank" >10.1007/978-3-642-36763-2_16</a>
Alternative languages
Result language
angličtina
Original language name
Planar Graphs as VPG-Graphs
Original language description
A graph is B(k) -VPG when it has an intersection representation by paths in a rectangular grid with at most k bends (turns). It is known that all planar graphs are B(3) -VPG and this was conjectured to be tight. We disprove this conjecture by showing that all planar graphs are B(2) -VPG. We also show that the 4-connected planar graphs constitute a subclass of the intersection graphs of Z-shapes (i.e., a special case of B(2) -VPG). Additionally, we demonstrate that a B(2) -VPG representation of a planargraph can be constructed in O(n^3/2 ) time. We further show that the triangle-free planar graphs are contact graphs of: L-shapes, ?-shapes, vertical segments, and horizontal segments (i.e., a special case of contact B(1) -VPG). From this proof we obtaina new proof that bipartite planar graphs are a subclass of 2-DIR.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
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
Article name in the collection
Graph Drawing;20th International Symposium, GD 2012 Redmond, WA, USA, September 19-21, 2012 Revised Selected Papers
ISBN
978-3-642-36762-5
ISSN
0302-9743
e-ISSN
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Number of pages
13
Pages from-to
174-186
Publisher name
Springer
Place of publication
New York, NY, USA
Event location
Redmond
Event date
Sep 19, 2012
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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