Coloring semi-random graphs in polynomial expected time

We present algorithms for coloring k-colorable semi-random graphs in polynomial expected time. The semi-random graphs are drawn from the $G_{SB}(n,p,k)$model. This model was introduced by A. Blum (1990) and with respect to randomness, this model lies between the random model G(n,p,k) where all edges are chosen with equal probability and the worst-case model. In this model, an adversary splits the n vertices into k color classes, each of size Θ(n). Then, the adversary chooses an ordering of all edges {u,v} such that u and v belong to different color classes. Based on this ordering, he considers each edge for inclusion by picking a bias $P_{uv}$ between p and 1-p of a coin which is flipped to determine whether the edge {u,v} is placed in the graph. The later choices of the adversary may depend on the previous coin tosses. The probability p is called the noise rate of the source. We give polynomial expected time algorithms for coloring semi-random graphs from $G_{SB}$(n,p,k) for p⩾$n^{-\alpha+&epsiv}$;, where α=(2k)/((k-1)(k+2)) and ϵ>0 is any constant. The semi-random model is a generalization of the random model G(n,p,k) and hence it is more difficult to develop algorithms for coloring semi-random graphs. Ours is the first result of this kind for the semi-random mode