Universal point subsets for planar graphs
Uloženo v:
| Název: | Universal point subsets for planar graphs |
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| Autoři: | Angelini, Patrizio, Binucci, Carla, Evans, William, Hurtado Díaz, Fernando Alfredo, Liotta, Giuseppe, Mchedlidze, Tamara, Meijer, Henk, Okamoto, Yoshio |
| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta |
| Informace o vydavateli: | Springer |
| Rok vydání: | 2012 |
| Sbírka: | Universitat Politècnica de Catalunya, BarcelonaTech: UPCommons - Global access to UPC knowledge |
| Témata: | Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria convexa i discreta, Discrete geometry, Geometria discreta, Classificació AMS::52 Convex and discrete geometry::52C Discrete geometry |
| Popis: | A set S of k points in the plane is a universal point subset for a class G of planar graphs if every graph belonging to G admits a planar straight-line drawing such that k of its vertices are represented by the points of S . In this paper we study the following main problem: For a given class of graphs, what is the maximum k such that there exists a universal point subset of size k ? We provide a ⌈ √ n ⌉ lower bound on k for the class of planar graphs with n ver- tices. In addition, we consider the value F ( n; G ) such that every set of F ( n; G ) points in general position is a universal subset for all graphs with n vertices be- longing to the family G , and we establish upper and lower bounds for F ( n; G ) for different families of planar graphs, including 4-connected planar graphs and nested-triangles graphs. ; Peer Reviewed ; Postprint (author’s final draft) |
| Druh dokumentu: | conference object |
| Popis souboru: | 10 p.; application/pdf |
| Jazyk: | English |
| Relation: | http://link.springer.com/chapter/10.1007/978-3-642-35261-4_45; http://hdl.handle.net/2117/18077 |
| DOI: | 10.1007/978-3-642-35261-4_45 |
| Dostupnost: | http://hdl.handle.net/2117/18077 https://doi.org/10.1007/978-3-642-35261-4_45 |
| Rights: | Attribution-NonCommercial-NoDerivs 3.0 Spain ; http://creativecommons.org/licenses/by-nc-nd/3.0/es/ ; Open Access |
| Přístupové číslo: | edsbas.CFAA49E |
| Databáze: | BASE |
Nájsť tento článok vo Web of Science | Abstrakt: | A set S of k points in the plane is a universal point subset for a class G of planar graphs if every graph belonging to G admits a planar straight-line drawing such that k of its vertices are represented by the points of S . In this paper we study the following main problem: For a given class of graphs, what is the maximum k such that there exists a universal point subset of size k ? We provide a ⌈ √ n ⌉ lower bound on k for the class of planar graphs with n ver- tices. In addition, we consider the value F ( n; G ) such that every set of F ( n; G ) points in general position is a universal subset for all graphs with n vertices be- longing to the family G , and we establish upper and lower bounds for F ( n; G ) for different families of planar graphs, including 4-connected planar graphs and nested-triangles graphs. ; Peer Reviewed ; Postprint (author’s final draft) |
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| DOI: | 10.1007/978-3-642-35261-4_45 |