Planar Graphs as VPG-Graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10190756" target="_blank" >RIV/00216208:11320/13:10190756 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.7155/jgaa.00300" target="_blank" >http://dx.doi.org/10.7155/jgaa.00300</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.7155/jgaa.00300" target="_blank" >10.7155/jgaa.00300</a>

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
—
Czech description
—

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

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)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)