devn00b
/
EQ2EMu


			
							123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126
							<html><head><!-- Copyright 2007 Aaron Windsor
     
     Distributed under the Boost Software License, Version 1.0.
     (See accompanying file LICENSE_1_0.txt or copy at
     http://www.boost.org/LICENSE_1_0.txt)
    
  -->
<title>Boost Graph Library: is_kuratowski_subgraph</title>
</head>
<body alink="#ff0000" 
      bgcolor="#ffffff" 
      link="#0000ee" 
      text="#000000" 
      vlink="#551a8b"> 
<img src="../../../boost.png" alt="C++ Boost" height="86" width="277"> 

<br clear="">

<h1><tt>is_kuratowski_subgraph</tt></h1>

<pre>template &lt;typename Graph, typename ForwardIterator, typename VertexIndexMap&gt;
bool is_kuratowski_subgraph(const Graph&amp; g, ForwardIterator begin, ForwardIterator end, VertexIndexMap vm)
</pre>

<p>

<tt>is_kuratowski_subgraph(g, begin, end)</tt> returns <tt>true</tt> exactly 
when the sequence of edges defined by the range <tt>[begin, end)</tt> forms a 
<a href="./planar_graphs.html#kuratowskisubgraphs"> Kuratowski subgraph</a> in 
the graph <tt>g</tt>. If you need to verify that an arbitrary graph has a 
<i>K<sub>5</sub></i> or <i>K<sub>3,3</sub></i> minor,  you should use the 
function <tt><a href="boyer_myrvold.html">boyer_myrvold_planarity_test</a></tt>
to isolate such a minor instead of this function. <tt>is_kuratowski_subgraph
</tt> exists to aid in testing and verification of the function 
<tt>boyer_myrvold_planarity_test</tt>, and for that reason, it expects its 
input to be a restricted set of edges forming a Kuratowski subgraph, as 
described in detail below.
<p>
<tt>is_kuratowski_subgraph</tt> creates a temporary graph out of the sequence 
of edges given and repeatedly contracts edges until it ends up with a graph 
with either all edges of degree 3 or all edges of degree 4. The final 
contracted graph is then checked against <i>K<sub>5</sub></i> or
<i>K<sub>3,3</sub></i> using the Boost Graph Library's 
<a href="isomorphism.html">isomorphism</a>
function. The contraction process starts by choosing edges adjacent to a vertex
of degree 1 and contracting those. When none are left, it moves on to edges 
adjacent to a vertex of degree 2. If only degree 3 vertices are left after this
stage, the graph is checked against <i>K<sub>3,3</sub></i>. Otherwise, if 
there's at least one degree 4 vertex, edges adjacent to degree 3 vertices are 
contracted as neeeded and the final graph is compared to <i>K<sub>5</sub></i>.
<p>
In order for this process to be deterministic, we make the following two 
restrictions on the input graph given to <tt>is_kuratowski_subgraph</tt>:
<ol>
<li>No edge contraction needed to produce a kuratowski subgraph results in 
multiple edges between the same pair of vertices (No edge <i>{a,b}</i> will be 
contracted at any point in the contraction process if <i>a</i> and <i>b</i> 
share a common neighbor.)
</li><li>If the graph contracts to a <i>K<sub>5</sub></i>, once the graph has 
been contracted to only vertices of degree at least 3, no cycles exist that 
contain solely degree 3 vertices.
</li></ol>
The second restriction is needed both to discriminate between targeting a 
<i>K<sub>5</sub></i> or a <i>K<sub>3,3</sub></i> and to determinstically 
contract the vertices of degree 4 once the <i>K<sub>5</sub></i> has been 
targeted. The Kuratowski subgraph output by the function <tt>
<a href="boyer_myrvold.html">boyer_myrvold_planarity_test</a></tt> is 
guaranteed to meet both of the above requirements.


<h3>Complexity</h3>

On a graph with <i>n</i> vertices, this function runs in time <i>O(n)</i>.

<h3>Where Defined</h3>

<p>
<a href="../../../boost/graph/is_kuratowski_subgraph.hpp">
<tt>boost/graph/is_kuratowski_subgraph.hpp</tt>
</a>

</p><h3>Parameters</h3>

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

<blockquote>
An undirected graph with no self-loops or parallel edges. The graph type must 
be a model of <a href="VertexListGraph.html">Vertex List Graph</a>.
</blockquote>

IN: <tt>ForwardIterator</tt> 

<blockquote>
A ForwardIterator with value_type 
<tt>graph_traits&lt;Graph&gt;::edge_descriptor</tt>.
</blockquote>

IN: <tt>VertexIndexMap vm</tt>

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


<h3>Example</h3>

<p>
<a href="../example/kuratowski_subgraph.cpp">
<tt>examples/kuratowski_subgraph.cpp</tt>
</a>

</p><h3>See Also</h3>

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


<br>
</p><hr>
Copyright © 2007 Aaron Windsor (<a href="mailto:aaron.windsor@gmail.com">
aaron.windsor@gmail.com</a>)
 
</body></html>