incomparabilityGraph -- produces the incomparability graph of a poset

Synopsis

Usage:

G = incomparabilityGraph P
Inputs:
- P, an instance of the type Poset
Outputs:
- G, an instance of the type Graph, which has an edge between two vertices if they are incomparable in $P$

Description

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 incomparable in $P$.

i1 : incomparabilityGraph booleanLattice 3

o1 = Graph{0 => {}       }
           1 => {2, 4, 6}
           2 => {1, 4, 5}
           3 => {4, 6, 5}
           4 => {1, 2, 3}
           5 => {2, 6, 3}
           6 => {1, 5, 3}
           7 => {}

o1 : Graph

Caveat

This method renames the vertices with integers $0, 1, \ldots$ corresponding to the index of the vertices in the GroundSet.

Ways to use `incomparabilityGraph` :

"incomparabilityGraph(Poset)"

For the programmer

The object incomparabilityGraph is a method function.