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

Research output: Contribution to journal › Article › peer-review

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
Externally published	Yes

Bibliographical 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. 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.

Funding

✩ 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.

Funders	Funder number
Gener-alitat de Catalunya
Comisión Interministerial de Ciencia y Tecnología	TIN2005-09198-C02-02, TIN2005-25859-E

Keywords

Coloring
Combinatorial problems
Distant-2 coloring
Graph algorithms
Random graphs

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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].",

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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].

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KW - Combinatorial problems

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

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Bibliographical note

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Keywords

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