  A Bely\u{\i} pair is a holomorphic map from a Riemann surface to $S^2$ with
additional properties. A dessin d'enfants is a bipartite graph with additional
structure. It is well know that there is a bijection between Bely\u{i} pairs
and dessins d'enfants.
  Vassiliev has defined a filtration on formal sums of isotopy classes of
knots. Motivated by this, we define a filtration on formal sums of Bely\u{\i}
pairs, and another on dessin d'enfants. We ask if the two definitions give the
same filtration.
