Graphs with large total angular resolution
The total angular resolution of a straight-line drawing is the minimum angle between two edges of the drawing. It combines two properties contributing to the readability of a drawing: the angular resolution, which is the minimum angle between incident edges, and the crossing resolution, which is the...
| Autores: | , , , , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/404001 |
| Acceso en línea: | https://hdl.handle.net/2117/404001 https://dx.doi.org/10.1016/j.tcs.2022.12.010 |
| Access Level: | acceso abierto |
| Palabra clave: | Computer science--Mathematics Graph theory Graph drawing Total angular resolution Angular resolution Crossing resolution NP-hardness. Informàtica--Matemàtica Grafs, Teoria de Classificació AMS::68 Computer science::68R Discrete mathematics in relation to computer science Classificació AMS::05 Combinatorics::05C Graph theory Àrees temàtiques de la UPC::Matemàtiques i estadística Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
| Sumario: | The total angular resolution of a straight-line drawing is the minimum angle between two edges of the drawing. It combines two properties contributing to the readability of a drawing: the angular resolution, which is the minimum angle between incident edges, and the crossing resolution, which is the minimum angle between crossing edges. We consider the total angular resolution of a graph, which is the maximum total angular resolution of a straight-line drawing of this graph. We prove tight bounds for the number of edges for graphs for some values of the total angular resolution up to a finite number of well specified exceptions of constant size. In addition, we show that deciding whether a graph has total angular resolution at least is NP-hard. Further we present some special graphs and their total angular resolution. |
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