Saturated simple and k-simple topological graphs

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Saturated simple and k-simple topological graphs

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Saturated simple and k-simple topological graphs

Popis výsledku anglicky

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.

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

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

Computational Geometry: Theory and Applications

ISSN

0925-7721

e-ISSN

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Svazek periodika

48

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

16

Strana od-do

295-310

Kód UT WoS článku

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EID výsledku v databázi Scopus

2-s2.0-84912574797