Geometric tree graphs of points in convex position
Given a set $P$ of points in the plane, the geometric tree graph of $P$ is defined as the graph $T(P)$ whose vertices are non-crossing rectilinear spanning trees of $P$, and where two trees $T_1$ and $T_2$ are adjacent if $T_2 = T_1 -e+f$ for some edges $e$ and $f$. In this paper we concentrate on t...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 1997 |
| 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:2117/959 |
| Acceso en línea: | https://hdl.handle.net/2117/959 |
| Access Level: | acceso abierto |
| Palabra clave: | Convex geometry Computing Methodologies Graph theory Convex Position Geometria convexa Informàtica Ciències de la computació Grafs, Teoria de Classificació AMS::05 Combinatorics::05C Graph theory Classificació AMS::52 Convex and discrete geometry::52A General convexity Classificació AMS::68 Computer science::68U Computing methodologies and applications |
| Sumario: | Given a set $P$ of points in the plane, the geometric tree graph of $P$ is defined as the graph $T(P)$ whose vertices are non-crossing rectilinear spanning trees of $P$, and where two trees $T_1$ and $T_2$ are adjacent if $T_2 = T_1 -e+f$ for some edges $e$ and $f$. In this paper we concentrate on the geometric tree graph of a set of $n$ points in convex position, denoted by $G_n$. We prove several results about $G_n$, among them the existence of Hamilton cycles and the fact that they have maximum connectivity. |
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