The Parametrized Complexity of the Segment Number
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10475898" target="_blank" >RIV/00216208:11320/24:10475898 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/978-3-031-49275-4_7" target="_blank" >https://doi.org/10.1007/978-3-031-49275-4_7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-031-49275-4_7" target="_blank" >10.1007/978-3-031-49275-4_7</a>
Alternative languages
Result language
angličtina
Original language name
The Parametrized Complexity of the Segment Number
Original language description
Given a straight-line drawing of a graph, a segment is a maximal set of edges that form a line segment. Given a planar graph G, the segment number of G is the minimum number of segments that can be achieved by any planar straight-line drawing of G. The line cover number of G is the minimum number of lines that support all the edges of a planar straight-line drawing of G. Computing the segment number or the line cover number of a planar graph is-complete and, thus, NP-hard. We study the problem of computing the segment number from the perspective of parameterized complexity. We show that this problem is fixed-parameter tractable with respect to each of the following parameters: the vertex cover number, the segment number, and the line cover number. We also consider colored versions of the segment and the line cover number.
Czech name
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Czech description
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Classification
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)
Result continuities
Project
<a href="/en/project/GX23-04949X" target="_blank" >GX23-04949X: Fundamental questions of discrete geometry</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Graph Drawing and Network Visualization 31st International Symposium, GD 2023, Isola delle Femmine, Palermo, Italy, September 20–22, 2023, Revised Selected Papers, Part II
ISBN
978-3-031-49274-7
ISSN
0302-9743
e-ISSN
1611-3349
Number of pages
17
Pages from-to
97-113
Publisher name
Springer
Place of publication
Cham
Event location
Palermo, Italie
Event date
Sep 20, 2023
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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