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

Josep Díaz; Zvi Lotker; Maria Serna

doi:10.1016/j.ipl.2007.10.015

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

Josep Díaz, Zvi Lotker, Maria Serna

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3 Scopus citations

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 Θ (log n) with high probability. The result on random geometric graphs is extended to the random sector graphs defined in [J. Díaz, J. Petit, M. Serna. A random graph model for optical networks of sensors, IEEE Transactions on Mobile Computing 2 (2003) 143-154].

Original language	English
Pages (from-to)	144-148
Number of pages	5
Journal	Information Processing Letters
Volume	106
Issue number	4
DOIs	https://doi.org/10.1016/j.ipl.2007.10.015
State	Published - 16 May 2008

Keywords

Coloring
Combinatorial problems
Distant-2 coloring
Graph algorithms
Random graphs

ASJC Scopus subject areas

Theoretical Computer Science
Signal Processing
Information Systems
Computer Science Applications

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10.1016/j.ipl.2007.10.015

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title = "The distant-2 chromatic number of random proximity and random geometric graphs",

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 Θ (log n) with high probability. The result on random geometric graphs is extended to the random sector graphs defined in [J. D{\'i}az, J. Petit, M. Serna. A random graph model for optical networks of sensors, IEEE Transactions on Mobile Computing 2 (2003) 143-154].",

keywords = "Coloring, Combinatorial problems, Distant-2 coloring, Graph algorithms, Random graphs",

author = "Josep D{\'i}az and Zvi Lotker and Maria Serna",

note = "Funding Information: ✩ Partially supported by the FET pro-actives Integrated Project 15964 (AEOLUS) and by the Spanish CICYT projects TIN2005-09198-C02-02 (ASCE) and TIN2005-25859-E. * Corresponding author. E-mail addresses: [email protected] (J. D{\'i}az), [email protected] (Z. Lotker), [email protected] (M. Serna). 1 Partially supported by the Distinci{\'o} per a la Recerca de la Gener-alitat de Catalunya.",

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doi = "10.1016/j.ipl.2007.10.015",

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AU - Díaz, Josep

AU - Lotker, Zvi

AU - Serna, Maria

N1 - Funding Information: ✩ Partially supported by the FET pro-actives Integrated Project 15964 (AEOLUS) and by the Spanish CICYT projects TIN2005-09198-C02-02 (ASCE) and TIN2005-25859-E. * Corresponding author. E-mail addresses: [email protected] (J. Díaz), [email protected] (Z. Lotker), [email protected] (M. Serna). 1 Partially supported by the Distinció per a la Recerca de la Gener-alitat de Catalunya.

PY - 2008/5/16

Y1 - 2008/5/16

N2 - 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 Θ (log n) with high probability. The result on random geometric graphs is extended to the random sector graphs defined in [J. Díaz, J. Petit, M. Serna. A random graph model for optical networks of sensors, IEEE Transactions on Mobile Computing 2 (2003) 143-154].

AB - 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 Θ (log n) with high probability. The result on random geometric graphs is extended to the random sector graphs defined in [J. Díaz, J. Petit, M. Serna. A random graph model for optical networks of sensors, IEEE Transactions on Mobile Computing 2 (2003) 143-154].

KW - Coloring

KW - Combinatorial problems

KW - Distant-2 coloring

KW - Graph algorithms

KW - Random graphs

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

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Keywords

ASJC Scopus subject areas

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