Improved enumeration of simple topological graphs

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Improved enumeration of simple topological graphs

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

Improved enumeration of simple topological graphs

Popis výsledku anglicky

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

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GEGIG%2F11%2FE023" target="_blank" >GEGIG/11/E023: Kreslení grafů a jejich geometrické reprezentace</a><br>

Návaznosti

S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2013

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Discrete and Computational Geometry

ISSN

0179-5376

e-ISSN

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Svazek periodika

50

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

44

Strana od-do

727-770

Kód UT WoS článku

000324494500008

EID výsledku v databázi Scopus

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