  The classical Matrix-Tree Theorem allows one to list the spanning trees of a
graph by monomials in the expansion of the determinant of a certain matrix. We
prove that in the case of three-graphs (that is, hypergraphs whose edges have
exactly three vertices) the spanning trees are generated by the Pfaffian of a
suitably defined matrix. This result can be interpreted topologically as an
expression for the lowest order term of the Alexander-Conway polynomial of an
algebraically split link. We also prove some algebraic properties of our
Pfaffian-tree polynomial.
