The dimer problem and the Kirchhoff theorem

Application of the Kirchhoff theorem to lattice statistics leads to solution of the two-dimensional dimer problem, earlier obtained by the Pfaffian method. It is shown that the relation between the theory of network of linear resistors and the dimer problem is particularly useful in the threedimensional case. A number of dimer configurations on a decorated diamond lattice is found by calculating spanning trees on the corresponding lattice. The Kirchhoff theorem is proved in the spirit of the combinatorical solution of the Ising model.