List all (s,t)-cuts of a graph
List all (s,t)-cuts in a directed graph.
stCuts(graph, source, target)
- The input graph. It must be directed.
- The source vertex.
- The target vertex.
Given a $G$ directed graph and two, different and non-ajacent vertices, $s$ and $t$, an $(s,t)$-cut is a set of edges, such that after removing these edges from $G$ there is no directed path from $s$ to $t$.
- A list with entries:
cuts A list of numeric vectors containing edge ids. Each vector is an $(s,t)$-cut. partition1s A list of numeric vectors containing vertex ids, they correspond to the edge cuts. Each vertex set is a generator of the corresponding cut, i.e. in the graph $G=(V,E)$, the vertex set $X$ and its complementer $V-X$, generates the cut that contains exactly the edges that go from $X$ to $V-X$.
- Edge cuts
JS Provan and DR Shier: A Paradigm for listing (s,t)-cuts in graphs, Algorithmica 15, 351--372, 1996.
stMincuts to list all minimum cuts.
# A very simple graph g <- graph.formula(a -+ b -+ c -+ d -+ e) stCuts(g, source="a", target="e") # A somewhat more difficult graph g2 <- graph.formula(s --+ a:b, a:b --+ t, a --+ 1:2:3, 1:2:3 --+ b) stCuts(g2, source="s", target="t")