PROXIMITY GRAPHS: E, δ, Δ, χ AND ω-Reference-Cited by-同舟云学术

PROXIMITY GRAPHS: E, δ, Δ, χ AND ω

Published:2012-10 Issue:05 Volume:22 Page:439-469
ISSN:0218-1959
Container-title:International Journal of Computational Geometry & Applications
language:en
Short-container-title:Int. J. Comput. Geom. Appl.

Author:

BOSE PROSENJIT¹,DUJMOVIĆ VIDA¹,HURTADO FERRAN²,IACONO JOHN³,LANGERMAN STEFAN⁴,MEIJER HENK⁵,SACRISTÁN VERA⁶,SAUMELL MARIA⁷,WOOD DAVID R.⁸

Affiliation:

1. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario K1S 5B6, Canada

2. Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya Edifici Omega, Campus Nord, Jordi Girona 1-3, 08034 Barcelona, Spain

3. Department of Computer Science and Engineering, Polytechnic Institute of New York University, 5 MetroTech Center, Brooklyn, NY 11201, USA

4. Maître de recherches du F.R.S.-FNRS. Département d'Informatique, Université Libre de Bruxelles, ULB CP212, 50 Av. F.D. Roosevelt, 1050 Brussels, Belgium

5. Science Department, Roosevelt Academy, P. O. Box 94, NL-4330 AB Middelburg, The Netherlands

6. Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Edifici Omega, Campus Nord, Jordi Girona 1-3, 08034 Barcelona, Spain

7. Department of Applied Mathematics, Charles University Malostranské nám. 25, 118 00 Praha 1, Czech Republic

8. Department of Mathematics and Statistics, The University of Melbourne, Australia

Abstract

Graph-theoretic properties of certain proximity graphs defined on planar point sets are investigated. We first consider some of the most common proximity graphs of the family of the Delaunay graph, and study their number of edges, minimum and maximum degree, clique number, and chromatic number. In the second part of the paper we focus on the higher order versions of some of these graphs and give bounds on the same parameters.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218195912500112

Reference27 articles.

1. Relative neighborhood graphs and their relatives

2. Properties of some Euclidean proximity graphs

3. Properties of Gabriel Graphs Relevant to Geographic Variation Research and the Clustering of Points in the Plane

4. Transitions in geometric minimum spanning trees

5. The relative neighbourhood graph of a finite planar set

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