isComparabilityGraph -- determines if a graph is the comparability graph of a poset

Synopsis

Usage:

i = isComparabilityGraph G
Inputs:
- G, a graph,
Outputs:
- i, a Boolean value, whether $G$ is a comparability graph of a poset

Description

A Graph $G$ is a comparabilityGraph of a poset if it is has a transitiveOrientation.

i1 : G = comparabilityGraph booleanLattice 5;

i2 : isComparabilityGraph G

o2 = true

However, a non-triangular odd cycle is never a comparability graph.

i3 : G = graph {{1,2}, {2,3}, {3,4}, {4,5}, {1,5}};

i4 : isComparabilityGraph G

o4 = false

This method calls transitiveOrientation and checks that an error is not thrown. See the documentation for that method for a note on the implemented algorithm.

Ways to use isComparabilityGraph :

isComparabilityGraph(Graph)

For the programmer

The object isComparabilityGraph is a method function.

isComparabilityGraph -- determines if a graph is the comparability graph of a poset

Synopsis

Description

See also

Ways to use isComparabilityGraph :

For the programmer