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We give an algorithmic computation for the height of Kauffman's clock latticeobtained from a knot diagram with two adjacent regions starred and withoutcrossing information specified. We show that this lattice is more familiarlythe graph of perfect matchings of a bipartite graph obtained from the knotdiagram by overlaying the two dual Tait graphs of the knot diagram. Thissetting also makes evident applications to Chebyshev or harmonic knots, whoserelated bipartite graph is the popular grid graph, and to discrete Morsefunctions. Furthermore we prove structural properties of the bipartite graph ingeneral.

Kauffman's clock lattice as a graph of perfect matchings: a formula for its height