The distant-2 chromatic number of random proximity and random geometric graphs

Authors:
Josep Díaz;Zvi Lotker;Maria Serna
Affiliations:
LSI Department, Universitat Politècnica de Catalunya, Barcelona, Spain;Communication Systems Dept., Ben Gurion University, Beer Sheva, Israel;LSI Department, Universitat Politècnica de Catalunya, Barcelona, Spain
Venue:
Information Processing Letters
Year:
2008

Citing 7
Cited 0

Randomized algorithms

Randomized algorithms
A Random Graph Model for Optical Networks of Sensors

IEEE Transactions on Mobile Computing
The number of neighbors needed for connectivity of wireless networks

Wireless Networks
The chromatic and clique numbers of random scaled sector graphs

Theoretical Computer Science - Graph colorings
A bound on the chromatic number of the square of a planar graph

Journal of Combinatorial Theory Series B
Coloring the square of a planar graph

Journal of Graph Theory
A general framework for coloring problems: old results, new results, and open problems

IJCCGGT'03 Proceedings of the 2003 Indonesia-Japan joint conference on Combinatorial Geometry and Graph Theory

Quantified Score

Hi-index	0.89

Visualization

Abstract

We are interested in finding bounds for the distant-2 chromatic number of geometric graphs drawn from different models. We consider two undirected models of random graphs: random geometric graphs and random proximity graphs for which sharp connectivity thresholds have been shown. We are interested in a.a.s. connected graphs close just above the connectivity threshold. For such subfamilies of random graphs we show that the distant-2-chromatic number is @Q(logn) with high probability. The result on random geometric graphs is extended to the random sector graphs defined in [J. Diaz, J. Petit, M. Serna. A random graph model for optical networks of sensors, IEEE Transactions on Mobile Computing 2 (2003) 143-154].