# `make_maximal_planar`

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

A planar graph G is maximal planar if no additional edges (except parallel edges and self-loops) can be added to G without creating a non-planar graph. By Euler's formula, a maximal planar graph on n vertices (n > 2) always has 3n - 6 edges and 2n - 4 faces. The input graph to `make_maximal_planar` must be a biconnected planar graph with at least 3 vertices.

The default behavior of `make_maximal_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` maximal planar. 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_maximal_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 Readable Property Map that models the PlanarEmbedding concept.

IN: `VertexIndexMap vm`

> A Readable Property Map that maps vertices from `g` to distinct integers in the range `[0, num_vertices(g) )`
> Default: `get(vertex_index,g)`

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 vis`

> 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 graph with n vertices and m edges, `make_maximal_planar` runs in time O(n + m)

### Example

`examples/make_maximal_planar.cpp`

### See Also

Planar Graphs in the Boost Graph Library

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