Bounded Stub Resolution for Some Maximal 1-Planar Graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10386670" target="_blank" >RIV/00216208:11320/18:10386670 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/chapter/10.1007%2F978-3-319-74180-2_18" target="_blank" >https://link.springer.com/chapter/10.1007%2F978-3-319-74180-2_18</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-319-74180-2_18" target="_blank" >10.1007/978-3-319-74180-2_18</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Bounded Stub Resolution for Some Maximal 1-Planar Graphs

Popis výsledku v původním jazyce

The resolution of a drawing plays a crucial role when defining criteria for its quality and readability. In the past, grid resolution, edge-length resolution, angular resolution and crossing resolution have been investigated. We continue the study of the recently introduced stub resolution as an additional aesthetic criterion for nonplanar drawings of graphs. 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 containing that stub, over all the edges of the drawing. As a meaningful graph class, where crossings are naturally involved, we consider 1-planar graphs (i.e., graphs that allow planar drawings in which every edge is crossed at most once). In an attempt to prove the conjecture that the stub resolution of 1-planar graphs is bounded, we closely investigate a class of maximal 1-planar graphs arising from double-wheels. We show that each such graph allows a straight-line 1-planar drawing with stub resolution 1/5.

Název v anglickém jazyce

Bounded Stub Resolution for Some Maximal 1-Planar Graphs

Popis výsledku anglicky

The resolution of a drawing plays a crucial role when defining criteria for its quality and readability. In the past, grid resolution, edge-length resolution, angular resolution and crossing resolution have been investigated. We continue the study of the recently introduced stub resolution as an additional aesthetic criterion for nonplanar drawings of graphs. 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 containing that stub, over all the edges of the drawing. As a meaningful graph class, where crossings are naturally involved, we consider 1-planar graphs (i.e., graphs that allow planar drawings in which every edge is crossed at most once). In an attempt to prove the conjecture that the stub resolution of 1-planar graphs is bounded, we closely investigate a class of maximal 1-planar graphs arising from double-wheels. We show that each such graph allows a straight-line 1-planar drawing with stub resolution 1/5.

Druh

D - Stať ve sborníku

CEP obor

—

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/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Centrum excelence - Institut teoretické informatiky (CE-ITI)</a><br>

Návaznosti

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

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název statě ve sborníku

Algorithms and Discrete Applied Mathematics

ISBN

978-3-319-74179-6

ISSN

—

e-ISSN

neuvedeno

Počet stran výsledku

7

Strana od-do

214-220

Název nakladatele

SPRINGER

Místo vydání

Cham

Místo konání akce

Guwahati, India

Datum konání akce

15. 2. 2018

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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