  Starting from a recently-introduced algebraic structure on spin foam models,
we define a Hopf algebra by dividing with an appropriate quotient. The
structure, thus defined, naturally allows for a mirror analysis of spin foam
models with quantum field theory, from a combinatorial point of view. A
grafting operator is introduced allowing for the equivalent of a
Dyson-Schwinger equation to be written. Non-trivial examples are explicitly
worked out. Finally, the physical significance of the results is discussed.
