Figure 1. Poset P and lattice D(P ) in thick light edges. Di-graph A and (the complement of) graph G(P,A) in dark.
Figure 2. Left: The lattice D(P ) from Figure 1 embedded ina product of three chains, and the graph G(P,A) from Figure1 embedded as an induced subgraph of the product of pathson those chains. Right: The usual labelling on the product ofchains showing D(P ) as P？ [1, 0]？ [2, 0].
Figure 3. Graph (left) with compatible lattice (right) but nocompatible distributive lattice.
Figure 4. Compatible pair (G,L), poset JL, and the graph red(A c)
Figure 5. The Game of Conjecture 6.15