Improved enumeration of 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%2F13%3A10145590" target="_blank" >RIV/00216208:11320/13:10145590 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00454-013-9535-8" target="_blank" >http://dx.doi.org/10.1007/s00454-013-9535-8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00454-013-9535-8" target="_blank" >10.1007/s00454-013-9535-8</a>
Alternative languages
Result language
angličtina
Original language name
Improved enumeration of simple topological graphs
Original language description
A simple topological graph T=(V(T), E(T)) is a drawing of a graph in the plane where every two edges have at most one common point (an endpoint or a crossing) and no three edges pass through a single crossing. Topological graphs G and H are isomorphic ifH can be obtained from G by a homeomorphism of the sphere, and weakly isomorphic if G and H have the same set of pairs of crossing edges. We generalize results of Pach and Toth and the author's previous results on counting different drawings of a graphunder both notions of isomorphism. We prove that for every graph G with n vertices, m edges and no isolated vertices the number of weak isomorphism classes of simple topological graphs that realize G is at most 2^{O(n^2 log (m/n))}, and at most 2^{O(mn^{1/2} log n)} if m<n^{3/2}. As a consequence we obtain a new upper bound 2^{O(n^{3/2} log n)} on the number of intersection graphs of n pseudosegments. We improve the upper bound on the number of weak isomorphism classes of simple complete
Czech name
—
Czech description
—
Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—
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<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Discrete and Computational Geometry
ISSN
0179-5376
e-ISSN
—
Volume of the periodical
50
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
44
Pages from-to
727-770
UT code for WoS article
000324494500008
EID of the result in the Scopus database
—