Ratios of Norms for Polynomials and Connected n-width Problems
  Let G be a bounded simply connected domain and E be a regular compact subset of G with connected complement. We investigate the asymptotic behavior of the Kolmogorov k-width, k=k(n), of the set of polynomials of degree at most n having the supremum norm at most 1 on G restricted to E in the space of continuous functions on E. 
V. A. Prokhorov, E. B. Saff, and M. Yattselev