On the structure of Kauffman bracket skein algebra of a surface

Suppose R is a commutative ring with identity and a fixed invertible element q1/2 such that q+q⁻¹ is invertible. For an oriented surface Σ, let S(Σ;R) denote the Kauffman bracket skein algebra of Σ over R. It is shown that to each embedded graph G⊂Σ satisfying that Σ G is homeomorphic to a disk and some other mild conditions, one can associate a generating set for S(Σ;R), and the ideal of defining relations is generated by relations of degree at most $6$ supported by certain small subsurfaces.