`make_biconnected_planar`

template <typename Graph, typename PlanarEmbedding, typename EdgeIndexMap, typename AddEdgeVisitor>
void make_biconnected_planar(Graph& g, PlanarEmbedding embedding, EdgeIndexMap em, AddEdgeVisitor& vis);

A graph *G* is biconnected if, for every pair of vertices *u,v* in
*G*, there is a cycle containing both *u* and *v*.
Alternatively, a graph is biconnected if it is connected and cannot be made
disconnected by removing any single vertex. `make_biconnected_planar`
takes a connected
planar graph `g` as input and adds zero
or more edges to make `g` biconnected while preserving planarity.

The default behavior of `make_biconnected_planar` is to modify the
graph `g` by calling `add_edge(u,v,g)` for every pair of
vertices *(u,v)* where an edge needs to be added to make `g`
biconnected. This behavior can be overriden by providing a vistor as the
`AddEdgeVisitor` parameter. The only requirement for an
`AddEdgeVisitor` is that it define a member function with the
following signature:

template <typename Graph, typename Vertex>
void visit_vertex_pair(Vertex u, Vertex v, Graph& g);

This event point can also be used as a hook to update the underlying edge
index map automatically as edges are added. See the
documentation for the AddEdgeVisitor
concept for more information.
### Where Defined

`boost/graph/make_biconnected_planar.hpp`

### Parameters

IN/OUT: `Graph& g`
An undirected graph. The graph type must be a model of Vertex List Graph, Incidence Graph, and
a Mutable Graph

IN: `PlanarEmbedding embedding`
A model of PlanarEmbedding.

IN: `EdgeIndexMap vm`
A Readable Property Map
that maps edges from `g` to distinct integers in the range
`[0, num_edges(g) )`

**Default**: `get(edge_index,g)`

IN: `AddEdgeVisitor`
A model of AddEdgeVisitor
.

**Default**: `default_add_edge_visitor`, a class defines
`visit_vertex_pair` to dispatch its calls to `add_edge`.

### Complexity

On a planar graph with *n* vertices, `make_biconnected_planar`
runs in time *O(n)*
### Example

`examples/make_biconnected_planar.cpp`

### See Also

Planar Graphs in the Boost Graph Library

Copyright © 2007 Aaron Windsor (
aaron.windsor@gmail.com)