  We derive an inductive, combinatorial definition of a polynomial-valued
regular isotopy invariant of links and tangled graphs. We show that the
invariant equals the Reshetikhin-Turaev invariant corresponding to the
exceptional simple Lie algebra G_2. It is therefore related to G_2 in the same
way that the HOMFLY polynomial is related to A_n and the Kauffman polynomial is
related to B_n, C_n, and D_n. We give parallel constructions for the other rank
2 Lie algebras and present some combinatorial conjectures motivated by the new
inductive definitions.
