Macaulay2 » Documentation
Packages » Graphs :: minimalVertexCuts
next | previous | forward | backward | up | index | toc

# minimalVertexCuts -- finds the minimal vertex cuts of a graph

- Usage:
    `C = minimalVertexCuts G`
- Inputs:
  - G, a graph,
- Outputs:
  - C, a list, the minimal vertex cuts of a graph

## Description

A vertex cut is a set of vertices that, when removed from a graph, make the graph have more than one component. The minimal vertex cuts are the only the vertex cuts removing only the smallest amount of vertices. If the graph is complete, it has no vertex cuts, so the method returns an empty list.

    i1 : G = graph({{1,2},{2,3},{3,1},{3,4},{4,5},{5,3}},EntryMode=>"edges");

    i2 : minimalVertexCuts G

    o2 = {{3}}

    o2 : List

## See also

- vertexCuts -- lists all the vertex cuts of a graph
- vertexConnectivity -- computes the vertex connectivity of a graph

## Ways to use minimalVertexCuts:

- `minimalVertexCuts(Graph)`

## For the programmer

The object minimalVertexCuts is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Graphs.m2:2934:0.