A dyadic N-sieve is the unit cube in Rd, d ≥ 2, with removed N dyadic subcubes. The next geometric-combinatorial problem is rooted in some questions of nonlinear approximation by splines and wavelets. How many ε-linked cubes (0 ≤ ε ≤ 1) is required to cover the N-sieve? The family of cubes is ε-linked if it can be linearly ordered so that measure of intersection for two adjacent cubes is bigger than ε multiplying by measure of their union. If at least one of removed cubes is not dyadic, the upper bound maybe arbitrarily large but here the upper bound depends on d and N (exponentially if ε > 0, and linearly in N if ε = 0). We explain in this lecture graph theoretic ideas behind the proof and application to a SobolevWhitney type inequality playing an essential role in nonlinear approximation.