comparabilityGraph -- produces the comparability graph of a poset

Synopsis

• Usage:

  G = comparabilityGraph P

• Inputs:

  • P, an object of class Poset
• Outputs:

  • G, an object of class Graph, which has an edge between two vertices if they are comparable in P

Description

i1 : comparabilityGraph booleanLattice 3

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

o1 : Graph

Caveat

See also

• compare -- compares two elements in a poset
• incomparabilityGraph -- produces the incomparability graph of a poset
• isComparabilityGraph -- determines if a graph is the comparability graph of a poset
• transitiveOrientation -- generates a poset whose comparability graph is the given graph