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A Spectral Technique for Coloring Random 3-Colorable Graphs
SIAM journal on computing (Print)
Let G 3n,p,3 be a random 3-colorable graph on a set of 3n vertices generated as follows. First, split the vertices arbitrarily into three equal color classes and then choose every pair of vertices of distinct color classes, randomly and independently, to be an edge with probability p. We describe a polynomial time algorithm that finds a proper 3-coloring of G 3n,p,3 with high probability, whenever p ≥ c/n, where c is a sufficiently large absolute constant. This settles a problem of Blum anddoi:10.1137/s0097539794270248 fatcat:uw6tu3q63bdrzgbxwlkqmdiixi