The Stub Resolution of 1-Planar Graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10420251" target="_blank" >RIV/00216208:11320/20:10420251 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/978-3-030-39881-1_15" target="_blank" >https://doi.org/10.1007/978-3-030-39881-1_15</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-030-39881-1_15" target="_blank" >10.1007/978-3-030-39881-1_15</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The Stub Resolution of 1-Planar Graphs

Popis výsledku v původním jazyce

The resolution of a drawing plays a crucial role when defining criteria for its quality. In the past, grid resolution, edge-length resolution, angular resolution and crossing resolution have been investigated. In this paper, we investigate the stub resolution, a recently introduced criterion for nonplanar drawings. A crossed edge is divided into parts, called stubs, which should not be too short for the sake of readability. Thus, the stub resolution of a drawing is defined as the minimum ratio between the length of a stub and the length of the entire edge, over all the edges of the drawing. We consider 1-planar graphs and we explore scenarios in which near optimal stub resolution, i.e. arbitrarily close to 1/2, can be obtained in drawings with zero, one, or two bends per edge, as well as further resolution criteria, such as angular and crossing resolution. In particular, our main contributions are as follows: (i) Every 1-planar graph with independent crossing edges has a straight-line drawing with near optimal stub resolution; (ii) Every 1-planar graph has a 1-bend drawing with near optimal stub resolution.

Název v anglickém jazyce

The Stub Resolution of 1-Planar Graphs

Popis výsledku anglicky

The resolution of a drawing plays a crucial role when defining criteria for its quality. In the past, grid resolution, edge-length resolution, angular resolution and crossing resolution have been investigated. In this paper, we investigate the stub resolution, a recently introduced criterion for nonplanar drawings. A crossed edge is divided into parts, called stubs, which should not be too short for the sake of readability. Thus, the stub resolution of a drawing is defined as the minimum ratio between the length of a stub and the length of the entire edge, over all the edges of the drawing. We consider 1-planar graphs and we explore scenarios in which near optimal stub resolution, i.e. arbitrarily close to 1/2, can be obtained in drawings with zero, one, or two bends per edge, as well as further resolution criteria, such as angular and crossing resolution. In particular, our main contributions are as follows: (i) Every 1-planar graph with independent crossing edges has a straight-line drawing with near optimal stub resolution; (ii) Every 1-planar graph has a 1-bend drawing with near optimal stub resolution.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GA18-19158S" target="_blank" >GA18-19158S: Algoritmické, strukturální a složitostní aspekty geometrických a dalších konfigurací</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název statě ve sborníku

WALCOM: Algorithms and Computation - 14th International Conference, WALCOM 2020

ISBN

978-3-030-39880-4

ISSN

0302-9743

e-ISSN

—

Počet stran výsledku

13

Strana od-do

170-182

Název nakladatele

Springer Nature Switzerland

Místo vydání

Cham

Místo konání akce

Singapur

Datum konání akce

31. 3. 2020

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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