The comparability graph of a poset $P$ is the Graph with vertices given by the ground set of $P$ and which has edges between two vertices if they are comparable in $P$.
i1 : comparabilityGraph booleanLattice 3 o1 = Graph{0 => {1, 2, 3, 4, 5, 6, 7}} 1 => {0, 3, 5, 7} 2 => {0, 3, 6, 7} 3 => {0, 1, 2, 7} 4 => {0, 5, 6, 7} 5 => {0, 1, 4, 7} 6 => {0, 2, 4, 7} 7 => {0, 1, 2, 3, 4, 5, 6} o1 : Graph |
This method renames the vertices with integers $0, 1, \ldots$ corresponding to the index of the vertices in the GroundSet.
The object comparabilityGraph is a method function.