Checks a flow for admissibility in a Graph
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Graph::admissibleFlow(G, f) checks if the
f is admissible in the Graph
to its vertices and their capacities.
Graph::admissibleFlow checks whether a given
flow is an admissible flow in the specified graph. A flow in a graph
is a table
the number of units flowing from vertex
i to vertex
the flow is admissible. Otherwise
FALSE is returned.
Graph::admissibleFlow does not check whether
the flow is admissible, if a flow from vertex
j is allowed to pass through other vertices.
See Example 2.
In a cyclic graph with default capacities (1), the flow with one unit flowing from each vertex to its successor is certainly admissible:
G1 := Graph::createCircleGraph([v1, v2, v3, v4]): Graph::admissibleFlow(G1, table([v1, v2] = 1, [v2, v3] = 1, [v3, v4] = 1, [v4, v1] = 1))
The flow must be specified in whole.
not include "hops", like skipping vertices in the path:
Graph::admissibleFlow(Graph::createCircleGraph([v1, v2, v3]), table([v1, v3] = 1))
The flow, specified in a table