  We give an algorithmic computation for the height of Kauffman's clock lattice
obtained from a knot diagram with two adjacent regions starred and without
crossing information specified. We show that this lattice is more familiarly
the graph of perfect matchings of a bipartite graph obtained from the knot
diagram by overlaying the two dual Tait graphs of the knot diagram. This
setting also makes evident applications to Chebyshev or harmonic knots, whose
related bipartite graph is the popular grid graph, and to discrete Morse
functions. Furthermore we prove structural properties of the bipartite graph in
general.
