Augmenting the connectivity of geometric graphs

Authors:
M. Abellanas;A. García;F. Hurtado;J. Tejel;J. Urrutia
Affiliations:
Dep. Matemática Aplicada, Universidad Politécnica de Madrid, 28660 Madrid, Spain;Dep. Métodos Estadísticos, IUMA, Universidad de Zaragoza, Pl. San Francisco s/n, 50009 Zaragoza, Spain;Dep. Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Jordi Girona 1-3, 08034 Barcelona, Spain;Dep. Métodos Estadísticos, IUMA, Universidad de Zaragoza, Pl. San Francisco s/n, 50009 Zaragoza, Spain;Instituto de Matemáticas, Universidad Nac. Aut. de México, Ciudad Universitaria, México D.F. C.P. 04510, Mexico
Venue:
Computational Geometry: Theory and Applications
Year:
2008

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Abstract

Let G be a connected plane geometric graph with n vertices. In this paper, we study bounds on the number of edges required to be added to G to obtain 2-vertex or 2-edge connected plane geometric graphs. In particular, we show that for G to become 2-edge connected, 2n3 additional edges are required in some cases and that 6n7 additional edges are always sufficient. For the special case of plane geometric trees, these bounds decrease to n2 and 2n3, respectively.