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We study the dependence of complexity of the independent set problem depending on the asymptotic growth of the packing number of graphs (as a function of the number of vertices). It is shown that under some natural assumptions this problem is solvable in polynomial time if and only if the order of growth of the packing number is not than higher the logarithm of the number of vertices.

The impact of the growth rate of the packing number of graphs on the computational complexity of the independent set problem