Macaulay2 » Documentation
Packages » Matroids :: is3Connected
next | previous | forward | backward | up | index | toc

# is3Connected -- whether a matroid is 3-connected

- Usage:
    `is3Connected M`
- Inputs:
  - M, a matroid,
- Outputs:
  - a Boolean value, 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

## See also

- isConnected(Matroid) -- whether a matroid is connected
- getSeparation -- finds a k-separation of a matroid
- sum2 -- 2-sum of matroids

## Ways to use is3Connected:

- `is3Connected(Matroid)`

## For the programmer

The object is3Connected is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Matroids/doc-Matroids.m2:1850:0.