Català   Castellano   English
 Empreu aquest identificador per citar o enllaçar aquest ítem: http://hdl.handle.net/2117/9615

Arxiu Descripció MidaFormat
 Citació: Abellanas, M. [et al.]. On structural and graph theoretic properties of higher order Delaunay graphs. "International journal of computational geometry and applications", Desembre 2009, vol. 19, núm. 6, p. 595-615. Títol: On structural and graph theoretic properties of higher order Delaunay graphs Autor: Abellanas, Manuel; Bose, Prosenjit; García López de Lacalle, Jesús; Hurtado Díaz, Fernando Alfredo ; Nicolás, Carlos M.; Ramos, Pedro A. Data: des-2009 Tipus de document: Article Resum: Given a set $\emph{P}$ of $\emph{n}$ points in the plane, the order-$\emph{k}$ Delaunay graph is a graph with vertex set $\emph{P}$ and an edge exists between two points p,q ∊ $\emph{P}$ when there is a circle through $\emph{p}$ and $\emph{q}$ with at most $\emph{k}$ other points of $\emph{P}$ in its interior. We provide upper and lower bounds on the number of edges in an order-$\emph{k}$ Delaunay graph. We study the combinatorial structure of the set of triangulations that can be constructed with edges of this graph. Furthermore, we show that the order-$\emph{k}$ Delaunay graph is connected under the flip operation when $\emph{k}$ ≤ 1 but not necessarily connected for other values of $\emph{k}$. If $\emph{P}$ is in convex position then the order-$\emph{k}$ Delaunay graph is connected for all $\emph{k}$ ≥ 0. We show that the order-$\emph{k}$ Gabriel graph, a subgraph of the order-$\emph{k}$ Delaunay graph, is Hamiltonian for $\emph{k}$ ≥ 15. Finally, the order-$\emph{k}$ Delaunay graph can be used to effciently solve a coloring problem with applications to frequency assignments in cellular networks. ISSN: 0218-1959 URI: http://hdl.handle.net/2117/9615 DOI: 10.1142/S0218195909003143 Versió de l'editor: http://www2.uah.es/pramos/Papers/k-dg-ijcga.pdf Apareix a les col·leccions: DCCG - Grup de recerca en geometria computacional, combinatoria i discreta. Articles de revistaDepartaments de Matemàtica Aplicada. Articles de revistaAltres. Enviament des de DRAC Comparteix: