@inproceedings{b73e5355c5bc430cbff7c344539dadcb,
title = "The condensation phase transition in random graph coloring",
abstract = "Based on a non-rigorous formalism called the {"}cavity method{"}, physicists have made intriguing predictions on phase transitions in discrete structures. One of the most remarkable ones is that in problems such as random κ-SAT or random graph κ-coloring, very shortly before the threshold for the existence of solutions there occurs another phase transition called condensation [Krzakala et al., PNAS 2007]. The existence of this phase transition seems to be intimately related to the difficulty of proving precise results on, e. g., the κ-colorability threshold as well as to the performance of message passing algorithms. In random graph κ-coloring, there is a precise conjecture as to the location of the condensation phase transition in terms of a distributional fixed point problem. In this paper we prove this conjecture, provided that κ exceeds a certain constant κ0.",
keywords = "Graph coloring, Message-passing algorithm, Phase transitions, Random graphs",
author = "Victor Bapst and Amin Coja-Oghlan and Samuel Hetterich and Felicia Ra{\ss}mann and Dan Vilenchik",
note = "Publisher Copyright: {\textcopyright} Prasad Raghavendra and Tselil Schramm.; 17th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2014 and the 18th International Workshop on Randomization and Computation, RANDOM 2014 ; Conference date: 04-09-2014 Through 06-09-2014",
year = "2014",
month = sep,
day = "1",
doi = "10.4230/LIPIcs.APPROX-RANDOM.2014.449",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
pages = "449--464",
editor = "Klaus Jansen and Rolim, {Jose D. P.} and Devanur, {Nikhil R.} and Cristopher Moore",
booktitle = "Leibniz International Proceedings in Informatics, LIPIcs",
address = "Germany",
}