comparabilityGraph -- produces the comparability graph of a poset

Synopsis

Usage:

G = comparabilityGraph 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 comparable 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 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

Caveat

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

Ways to use `comparabilityGraph` :

"comparabilityGraph(Poset)"

For the programmer

The object comparabilityGraph is a method function.