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On structural and graph theoretic properties of higher order Delaunay graphs
dc.contributor.author | Abellanas, Manuel |
dc.contributor.author | Bose, Prosenjit |
dc.contributor.author | García López de Lacalle, Jesús |
dc.contributor.author | Hurtado Díaz, Fernando Alfredo |
dc.contributor.author | Nicolás, Carlos M. |
dc.contributor.author | Ramos, Pedro A. |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II |
dc.date.accessioned | 2010-10-11T10:28:08Z |
dc.date.available | 2010-10-11T10:28:08Z |
dc.date.created | 2009-12 |
dc.date.issued | 2009-12 |
dc.identifier.citation | 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. |
dc.identifier.issn | 0218-1959 |
dc.identifier.uri | http://hdl.handle.net/2117/9615 |
dc.description.abstract | 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. |
dc.format.extent | 21 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
dc.subject.lcsh | Graph theory |
dc.subject.lcsh | Combinatorial analysis |
dc.subject.lcsh | Voronoi polygons |
dc.subject.lcsh | Triangulations |
dc.title | On structural and graph theoretic properties of higher order Delaunay graphs |
dc.type | Article |
dc.subject.lemac | Grafs, Teoria de |
dc.subject.lemac | Anàlisi combinatòria |
dc.subject.lemac | Voronoi, Polígons de |
dc.subject.lemac | Triangulació |
dc.contributor.group | Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta |
dc.identifier.doi | 10.1142/S0218195909003143 |
dc.relation.publisherversion | http://www2.uah.es/pramos/Papers/k-dg-ijcga.pdf |
dc.rights.access | Open Access |
local.identifier.drac | 3257481 |
dc.description.version | Postprint (published version) |
local.citation.author | Abellanas, M.; Bose, P.; García, J.; Hurtado, F.; Nicolás, C.; Ramos, P.A. |
local.citation.publicationName | International journal of computational geometry and applications |
local.citation.volume | 19 |
local.citation.number | 6 |
local.citation.startingPage | 595 |
local.citation.endingPage | 615 |
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