Saturated simple and k-simple topological graphs
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10284157" target="_blank" >RIV/00216208:11320/15:10284157 - isvavai.cz</a>
Result on the web
<a href="http://www.sciencedirect.com/science/article/pii/S0925772114001151/pdfft?md5=fa73a922ee909670fcb57b7b5a5eb546&pid=1-s2.0-S0925772114001151-main.pdf" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0925772114001151/pdfft?md5=fa73a922ee909670fcb57b7b5a5eb546&pid=1-s2.0-S0925772114001151-main.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.comgeo.2014.10.008" target="_blank" >10.1016/j.comgeo.2014.10.008</a>
Alternative languages
Result language
angličtina
Original language name
Saturated simple and k-simple topological graphs
Original language description
A simple topological graph G is a graph drawn in the plane so that any pair of edges have at most one point in common, which is either an endpoint or a proper crossing. G is called saturated if no further edge can be added without violating this condition. We construct saturated simple topological graphs with n vertices and O(n) edges. For every k>1, we give similar constructions for k-simple topological graphs, that is, for graphs drawn in the plane so that any two edges have at most k points in common. We show that in any k-simple topological graph, any two independent vertices can be connected by a curve that crosses each of the original edges at most 2k times. Another construction shows that the bound 2k cannot be improved. Several other related problems are also considered.
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
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2015
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
48
Issue of the periodical within the volume
4
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
16
Pages from-to
295-310
UT code for WoS article
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EID of the result in the Scopus database
2-s2.0-84912574797