#### A Spectral Approach to Analyzing Belief Propagation for 3-Coloring

##### Amin Coja-Oghlan, Elchanan Mossel, Dan Vilenchik

Contributing to the rigorous understanding of BP, in this paper we relate the convergence of BP to spectral properties of the graph. This encompasses a result for random graphs with a planted'' solution; thus, we obtain the first rigorous result on BP for graph coloring in the case of a complex graphical structure (as opposed to trees). In particular, the analysis shows how Belief Propagation breaks the symmetry between the $3!$ possible permutations of the color classes.

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