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...

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Detalles Bibliográficos
Autores: Hernando Martín, María del Carmen|||0000-0002-3864-6566, Hurtado Díaz, Fernando Alfredo|||0000-0002-0108-9671, Márquez Pérez, Alberto, Mora Giné, Mercè|||0000-0001-6923-0320, Noy Serrano, Marcos|||0000-0002-2399-1359
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
Descripción
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.