<?xml version="1.0" encoding="utf-8" ?> <!-- for emacs: -*- coding: utf-8 -*- -->
<!-- Apache may like this line in the file .htaccess: AddCharset utf-8 .html -->
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0 plus SVG 1.1//EN" "http://www.w3.org/2002/04/xhtml-math-svg/xhtml-math-svg-flat.dtd" >
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
<head><title>spanningTree -- returns a spanning tree of a graph</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="___Time__Limit.html">next</a> | <a href="_smallest__Cycle__Size.html">previous</a> | <a href="___Time__Limit.html">forward</a> | <a href="_smallest__Cycle__Size.html">backward</a> | up | <a href="index.html">top</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> | <a href="http://www.math.uiuc.edu/Macaulay2/">Macaulay2 web site</a></div>
</td>
</tr>
</table>
<hr/>
<div><h1>spanningTree -- returns a spanning tree of a graph</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>T = spanningTree(G)</tt></div>
</dd></dl>
</div>
</li>
<li><div class="single">Inputs:<ul><li><span><tt>G</tt>, <span>a <a href="___Graph.html">graph</a></span></span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><tt>T</tt>, <span>a <a href="___Graph.html">graph</a></span>, the spanning tree of G</span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div><div>This function returns a breadth first spanning tree of a graph.</div>
<table class="examples"><tr><td><pre>i1 : R = QQ[x_1..x_6];</pre>
</td></tr>
<tr><td><pre>i2 : C = cycle R; -- a 6-cycle</pre>
</td></tr>
<tr><td><pre>i3 : spanningTree C
o3 = Graph{edges => {{x , x }, {x , x }, {x , x }, {x , x }, {x , x }}}
1 2 3 4 4 5 1 6 5 6
ring => R
vertices => {x , x , x , x , x , x }
1 2 3 4 5 6
o3 : Graph</pre>
</td></tr>
<tr><td><pre>i4 : T = graph {x_1*x_2,x_2*x_3, x_1*x_4,x_1*x_5,x_5*x_6}; -- a tree (no cycles)</pre>
</td></tr>
<tr><td><pre>i5 : T == spanningTree T
o5 = true</pre>
</td></tr>
<tr><td><pre>i6 : G = graph {x_1*x_2,x_2*x_3,x_3*x_1,x_4*x_5,x_5*x_6,x_6*x_4}; -- two three cycles</pre>
</td></tr>
<tr><td><pre>i7 : spanningTree G
o7 = Graph{edges => {{x , x }, {x , x }, {x , x }, {x , x }}}
1 2 1 3 4 6 5 6
ring => R
vertices => {x , x , x , x , x , x }
1 2 3 4 5 6
o7 : Graph</pre>
</td></tr>
</table>
</div>
</div>
<div class="waystouse"><h2>Ways to use <tt>spanningTree</tt> :</h2>
<ul><li>spanningTree(Graph)</li>
</ul>
</div>
</div>
</body>
</html>
