On the Approximability of Independent Set Problem on Power Law Graphs

We give the first nonconstant lower bounds for the approximability of the Independent Set Problem on the Power Law Graphs. These bounds are of the form $n^{ϵ}$ in the case when the power law exponent satisfies $\beta <1$. In the case when $\beta =1$, the lower bound is of the form $\log (n{)}^{ϵ}$. The embedding technique used in the proof could also be of independent interest.