2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62204The 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.minor changes, 29 pages, version accepted for publication in Int. Math. Res. NoticesCombinatoricsGeometric TopologyQuantum Algebra05C50 (Primary); 15A15; 57M27 (Secondary)text