  Each ruling of a Legendrian link can be naturally treated as a surface. For
knots, the ruling is 2-graded if and only if the surface is orientable. For
2-graded rulings of homogeneous (in particular, alternating) knots, we prove
that the genus of this surface is at most the genus of the knot. While this is
not true in general, we do prove that the canonical genus (a.k.a. diagram
genus) of any knot is an upper bound for the genera of its 2-graded rulings.
