Determinant of links, spanning trees, and a theorem of Shank (Q2827426)

From the article's abstract: ``In this note, we first give an alternative elementary proof (using Kauffman's state model) of the relation between the determinant of a link and the spanning trees of the corresponding Tait graph (obtained by checkerboard coloring a link diagram associated to the link, so that the unbounded face is shaded, assigning a vertex to each shaded region, and an edge with a plus or minus sign to each crossing). Then, we use this relation to give an extremely short, knot theoretical proof of a theorem due to \textit{H. Shank} [Lect. Notes Math. 452, 42--54 (1975; Zbl 0307.05120)] stating that a link has component number one if and only if the number of spanning trees of its Tait graph is odd.''