Note on Min- k-Planar Drawings of Graphs

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F24%3A00139105" target="_blank" >RIV/00216224:14330/24:00139105 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.4230/LIPICS.GD.2024.8" target="_blank" >http://dx.doi.org/10.4230/LIPICS.GD.2024.8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPICS.GD.2024.8" target="_blank" >10.4230/LIPICS.GD.2024.8</a>

Result language

angličtina

Original language name

Note on Min- k-Planar Drawings of Graphs

Original language description

The k-planar graphs, which are (usually with small values of k such as 1,2,3) subject to recent intense research, admit a drawing in which edges are allowed to cross, but each one edge is allowed to carry at most k crossings. In recently introduced [Binucci et al., GD 2023] min-k-planar drawings of graphs, edges may possibly carry more than k crossings, but in any two crossing edges, at least one of the two must have at most k crossings. In both concepts, one may consider general drawings or a popular restricted concept of drawings called simple. In a simple drawing, every two edges are allowed to cross at most once, and any two edges which share a vertex are forbidden to cross. While, regarding the former concept, it is for k ≤ 3 known (but perhaps not widely known) that every general k-planar graph admits a simple k-planar drawing and this ceases to be true for any k ≤ 4, the difference between general and simple drawings in the latter concept is more striking. We prove that there exist graphs with a min-2-planar drawing, or with a min-3-planar drawing avoiding crossings of adjacent edges, which have no simple min-k-planar drawings for arbitrarily large fixed k.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

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OECD FORD branch

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

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

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

Article name in the collection

32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)

ISBN

9783959773430

ISSN

1868-8969

e-ISSN

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Number of pages

10

Pages from-to

„8:1“-„8:10“

Publisher name

Schloss Dagstuhl -- Leibniz-Zentrum f{"u}r Informatik

Place of publication

Dagstuhl, Germany

Event location

Wien, Austria

Event date

Jan 1, 2024

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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