is3Connected -- whether a matroid is 3-connected

Synopsis

• Usage:
is3Connected M
• Inputs:
• M,
• Outputs:
• , whether M is 3-connected

Description

A matroid M is called m-connected if M has no k-separations for k < m (see getSeparation for the definition of a k-separation). Thus a matroid is 3-connected if it has no 2-separations (or 1-separations).

 i1 : U1 = uniformMatroid(1, 4) o1 = a matroid of rank 1 on 4 elements o1 : Matroid i2 : isConnected U1 o2 = true i3 : is3Connected U1 o3 = false i4 : is3Connected matroid completeMultipartiteGraph {3,3} o4 = true