Evasiveness and the Distribution of Prime Numbers

@article{Babai2010EvasivenessAT,
  title={Evasiveness and the Distribution of Prime Numbers},
  author={L{\'a}szl{\'o} Babai and Anandam Banerjee and Raghav Kulkarni and Vipul Naik},
  journal={ArXiv},
  year={2010},
  volume={abs/1001.4829}
}
We confirm the eventual evasiveness of several classes of monotone graph properties under widely accepted number theoretic hypotheses. In particular we show that Chowla's conjecture on Dirichlet primes implies that (a) for any graph $H$, "forbidden subgraph $H$" is eventually evasive and (b) all nontrivial monotone properties of graphs with $\le n^{3/2-\epsilon}$ edges are eventually evasive. ($n$ is the number of vertices.) While Chowla's conjecture is not known to follow from the Extended… 

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