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DOI: 10.4230/LIPIcs.APPROX-RANDOM.2015.726
URN: urn:nbn:de:0030-drops-53321
URL: https://drops.dagstuhl.de/opus/volltexte/2015/5332/
Coja-Oghlan, Amin ; Efthymiou, Charilaos ; Jaafari, Nor
Local Convergence of Random Graph Colorings
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Abstract
Let G=G(n,m) be a random graph whose average degree d=2m/n is below the k-colorability threshold. If we sample a k-coloring Sigma of G uniformly at random, what can we say about the correlations between the colors assigned to vertices that are far apart? According to a prediction from statistical physics, for average degrees below the so-called condensation threshold d_c, the colors assigned to far away vertices are asymptotically independent [Krzakala et al: PNAS 2007]. We prove this conjecture for k exceeding a certain constant k_0. More generally, we determine the joint distribution of the k-colorings that Sigma induces locally on the bounded-depth neighborhoods of a fixed number of vertices.
BibTeX - Entry
@InProceedings{cojaoghlan_et_al:LIPIcs:2015:5332,
author = {Amin Coja-Oghlan and Charilaos Efthymiou and Nor Jaafari},
title = {{Local Convergence of Random Graph Colorings}},
booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
pages = {726--737},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-89-7},
ISSN = {1868-8969},
year = {2015},
volume = {40},
editor = {Naveen Garg and Klaus Jansen and Anup Rao and Jos{\'e} D. P. Rolim},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2015/5332},
URN = {urn:nbn:de:0030-drops-53321},
doi = {10.4230/LIPIcs.APPROX-RANDOM.2015.726},
annote = {Keywords: Random graph, Galton-Watson tree, phase transitions, graph coloring, Gibbs distribution, convergence}
}
| Keywords: | Random graph, Galton-Watson tree, phase transitions, graph coloring, Gibbs distribution, convergence | |
| Seminar: | Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015) | |
| Issue date: | 2015 | |
| Date of publication: | 13.08.2015 |
