# minimal.st.separators

From igraph v0.6.5-2
by Gabor Csardi

##### Minimum size vertex separators

List all vertex sets that are minimal (s,t) separators for some s and t, in an undirected graph.

- Keywords
- graphs

##### Usage

`minimal.st.separators(graph)`

##### Arguments

- graph
- The input graph. It may be directed, but edge directions are ignored.

##### Details

A $(s,t)$ vertex separator is a set of vertices, such that after their removal from the graph, there is no path between $s$ and $t$ in the graph.

A $(s,t)$ vertex separator is minimal if none of its subsets is an $(s,t)$ vertex separator.

##### Value

- A list of numeric vectors. Each vector contains a vertex set (defined by vertex ids), each vector is an (s,t) separator of the input graph, for some $s$ and $t$.

##### concept

- Minimal (s,t) separators
- Vertex separator

##### References

Anne Berry, Jean-Paul Bordat and Olivier Cogis: Generating All the
Minimal Separators of a Graph, In: Peter Widmayer, Gabriele Neyer
and Stephan Eidenbenz (editors): *Graph-theoretic concepts in
computer science*, 1665, 167--172, 1999. Springer.

##### Examples

```
ring <- graph.ring(4)
minimal.st.separators(ring)
chvatal <- graph.famous("chvatal")
minimal.st.separators(chvatal)
```

*Documentation reproduced from package igraph, version 0.6.5-2, License: GPL (>= 2)*

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