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<Title>Boost Graph Library: make_biconnected_planar</Title>
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<H1><tt>make_biconnected_planar</tt></H1>

<p>

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

<p>

A graph <i>G</i> is biconnected if, for every pair of vertices <i>u,v</i> in 
<i>G</i>, there is a cycle containing both <i>u</i> and <i>v</i>. 
Alternatively, a graph is biconnected if it is connected and cannot be made 
disconnected by removing any single vertex. <tt>make_biconnected_planar</tt> 
takes a <a href="./make_connected.html">connected</a> 
<a href="planar_graphs.html">planar</a> graph <tt>g</tt> as input and adds zero
or more edges to make <tt>g</tt> biconnected while preserving planarity.
<p>
The default behavior of <tt>make_biconnected_planar</tt> is to modify the 
graph <tt>g</tt> by calling <tt>add_edge(u,v,g)</tt> for every pair of 
vertices <i>(u,v)</i> where an edge needs to be added to make <tt>g</tt> 
biconnected. This behavior can be overriden by providing a vistor as the 
<tt>AddEdgeVisitor</tt> parameter. The only requirement for an 
<tt>AddEdgeVisitor</tt> is that it define a member function with the 
following signature:
<pre>
template &lt;typename Graph, typename Vertex&gt;
void visit_vertex_pair(Vertex u, Vertex v, Graph& g);
</pre>
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 <a href="./AddEdgeVisitor.html">AddEdgeVisitor</a> 
concept for more information.

<H3>Where Defined</H3>

<P>
<a href="../../../boost/graph/make_biconnected_planar.hpp">
<TT>boost/graph/make_biconnected_planar.hpp</TT>
</a>

<h3>Parameters</h3>

IN/OUT: <tt>Graph&amp; g</tt>

<blockquote>
An undirected graph. The graph type must be a model of <a
href="VertexListGraph.html">Vertex List Graph</a>, <a
href="IncidenceGraph.html">Incidence Graph</a>, and
a <a href="MutableGraph.html">Mutable Graph</a><br>
</blockquote>

IN: <tt>PlanarEmbedding embedding</tt>

<blockquote>
A model of <a href="PlanarEmbedding.html">PlanarEmbedding</a>.
</blockquote>

IN: <tt>EdgeIndexMap vm</tt>

<blockquote>
A <a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map
</a> that maps edges from <tt>g</tt> to distinct integers in the range 
<tt>[0, num_edges(g) )</tt><br>
<b>Default</b>: <tt>get(edge_index,g)</tt><br>
</blockquote>

IN: <tt>AddEdgeVisitor</tt>

<blockquote>
A model of <a href="AddEdgeVisitor.html">AddEdgeVisitor
</a>.<br>
<b>Default</b>: <tt>default_add_edge_visitor</tt>, a class defines 
<tt>visit_vertex_pair</tt> to dispatch its calls to <tt>add_edge</tt>.
</blockquote>


<h3>Complexity</h3>

On a planar graph with <i>n</i> vertices, <tt>make_biconnected_planar</tt> 
runs in time <i>O(n)</i>

<H3>Example</H3>

<P>
<a href="../example/make_biconnected_planar.cpp">
<TT>examples/make_biconnected_planar.cpp</TT>
</a>

<h3>See Also</h3>

<a href="planar_graphs.html">Planar Graphs in the Boost Graph Library</a>

<br>
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Copyright &copy; 2007 Aaron Windsor (<a href="mailto:aaron.windsor@gmail.com">
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