# minimal.st.separators

0th

Percentile

##### 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.

##### Aliases
• minimal.st.separators
##### 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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