# 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.