From dongxu@sciences.sdsu.edu  Tue Jun 19 02:25:55 2007
From: dongxu@sciences.sdsu.edu (Dong Xu)
Date: Mon, 18 Jun 2007 18:25:55 -0700
Subject: [compsci] Math Colloquium: Steven Butler, Fri., June 22, 2:00pm, GMCS 313
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Message-ID: <14da35910706181825r5ecdcce7w404bff35369d5ccc@mail.gmail.com>

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 Mathematics Colloquium

*Steven Butler
*U.C.S.D.

* Induced Universal Graphs

*Friday, June 22, 2007 =96 2:00pm - GMCS 313
 For a fixed (finite) family of graphs, a universal graph for that family i=
s
one in which all members of the family appear as a subgraph.  For example,
if we fix the family as all graphs on at most n vertices then the complete
graph K_n is a universal graph for that family.  An induced universal graph
is defined similarly, but now the subgraphs must be induced subgraphs.

We will give a construction of an induced universal graph for the family of
all graphs on n vertices with maximum degree at most r.  Our construction
will be explicit (i.e., no probabilistic tools needed) and the only tool we
will need to use is Hall's Marriage Theorem.

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<span class=3D"gmail_quote"><br><br></span>
<div>
<div align=3D"center">Mathematics Colloquium<br>
<br>
<b>Steven Butler<br>
</b>U.C.S.D.<br>
<br>
<i>&nbsp;Induced Universal Graphs<br>
<br>
</i>Friday, June 22, 2007 =96 2:00pm - GMCS 313<br>
</div>
<div>For a fixed (finite) family of graphs, a universal graph for that
family is one in which all members of the family appear as a
subgraph.&nbsp; For example, if we fix the family as all graphs on at
most n vertices then the complete graph K_n is a universal graph for
that family.&nbsp; An induced universal graph is defined similarly,
but now the subgraphs must be induced subgraphs.<br>
<br>
We will give a construction of an induced universal graph for the
family of all graphs on n vertices with maximum degree at most r.&nbsp;
Our construction will be explicit (i.e., no probabilistic tools
needed) and the only tool we will need to use is Hall&#39;s Marriage
Theorem.</div>
<div><br></div>
</div>
<br clear=3D"all">

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////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
//////////////////////