CaGe-website/fourreg.html at master · CaGe-graph/CaGe-website · GitHub

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<html>
<head>
<title>CaGe -- the 4-regular plane graphs windows</title>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
<link href="style.css" rel="stylesheet" type="text/css">
<script language="JavaScript" src="select.js">
</script>
<script language="JavaScript" src="navigate.js">
</script>
<script language="JavaScript" src="subwindow.js">
</script>
</head>
<body onUnload="closeSubwindow ();">
<table border="0" cellspacing="0" cellpadding="0" width="500">
  <tr valign="top">
    <td>
      <h1>The 4-regular plane graphs windows</h1>
    </td>
    <td rowspan="8"><img height="1" width="20" src="Images/trans.gif" alt=""></td>
  </tr>
  <tr valign="top">
    <td>
      <p>
4-regular plane graphs are plane graphs where every vertex has exactly 4 neighbours.
      4-regular graphs are sometimes also called &quot;quartic&quot;
      graphs.
      There are 2 different interfaces that allow to further specify the class of graphs that shall be
 generated.</p>
    </td>
    </td>
  </tr>
  <tr valign="top">
    <td>
	  <br>
	  <h2>All face sizes allowed</h2>
      <p>In this section one can generate 4-regular
	  plane graphs with a given number of vertices.
Furthermore one of the following three properties must be chosen:</p>
	  <ul>
		<li>3-connected</li>
		<li>4-edge-connected</li>
		<li>3-connected and cyclically 6-edge connected</li>
	  </ul>
<p>
A program for the generation of 4-regular plane graphs with 1- or 2-cuts will be future work.
</p>
    </td>
    <td><br>
      <a href="Images/4regallfaces.png" target="_blank" onClick="return imageWindow (this, 568, 530, '4-regular graph in TwoView');"><img src="Images/4regallfaces-small.gif" border="0" alt="4-regular graph in TwoView"></a></td>
  </tr>
  <tr valign="top">
    <td>
	  <br>
	  <h2>Quartic graphs with given face sizes</h2>
	  <a name="givenfaces"></a>
      <p>Just like for the case of <a href="trireg.html#givenfaces">cubic plane graphs with given face sizes</a>) you can specify which face sizes may occur in the generated graphs.</p>
	  <p>The generator used in this part is designed for the case of relatively many face sizes
	  allowed and does not allow extra options. For the future a reimplementation
  of the algorithm described in Discr. Appl. Math. 128, pages 541-554 is planned.
 This will
be applied in the case of few face sizes allowed.
</p>
    </td>
    <td><br>
      <a href="Images/4reg_allowedfaces.png" target="_blank" onClick="return imageWindow (this, 637, 676, '4-regular graph in Rasmol');"><img src="Images/4reg_allowedfaces-small.gif" border="0" alt="4-regular graph in Rasmol"></a></td>
  </tr>
  <tr valign="top">
    <td align="left"><font face="Verdana, Arial, Helvetica, sans-serif" size="2">&nbsp;</font></td>
  </tr>
  <tr valign="top">
    <td nowrap width="500">
      <table border="0" cellspacing="0%" cellpadding=0%" width="100%">
        <tr valign="top">
          <td align="right" nowrap><a href="generators.html" onMouseOver="return setFocused (this);" onMouseOut="setPassive (this);" onClick="return setClicked (this);" class="navigation">choosing
            a generator window<img src="Images/trans.gif" width=5 height=1 border="0" alt=" "><img src="Images/pointer-backward-passive.gif" width="6" height="11" border="0" alt="&lt;" name="generators"></a></td>
          <td nowrap width="100%" align="center">&nbsp;&nbsp;</td>
          <td align="left" nowrap><a href="output.html" onMouseOver="return setFocused (this);" onMouseOut="setPassive (this);" onClick="return setClicked (this);" class="navigation"><img src="Images/pointer-passive.gif" width="6" height="11" border="0" alt="&gt;" name="output"><img src="Images/trans.gif" width=5 height=1 border="0" alt=" ">output
            options</a></td>
        </tr>
        <tr>
          <td colspan="3" bgcolor="#ffffff"><img src="Images/trans.gif" width="1" height="1"></td>
        </tr>
        <tr valign="top">
          <td align="right" nowrap><a href="trireg.html" onMouseOver="return setFocused (this);" onMouseOut="setPassive (this);" onClick="return setClicked (this);" class="navigation">the
            3-regular plane graphs windows<img src="Images/trans.gif" width=5 height=1 border="0" alt=" "><img src="Images/pointer-backward-passive.gif" width="6" height="11" border="0" alt="&lt;" name="trireg"></a></td>
          <td nowrap width="100%" align="center">&nbsp;&nbsp;</td>
          <td align="left" nowrap><a href="hydrocarbons.html" onMouseOver="return setFocused (this);" onMouseOut="setPassive (this);" onClick="return setClicked (this);" class="navigation"><img src="Images/pointer-passive.gif" id="selecting" width="6" height="11" border="0" alt="&gt;" name="hydrocarbons"><img src="Images/trans.gif" width=5 height=1 border="0" alt=" ">the
            hydrocarbons windows</a></td>
        </tr>
      </table>
    </td>
  </tr>
  <tr>
    <td><img height="1" width="500" src="Images/trans.gif"></td>
  </tr>
</table>
<script language="JavaScript"><!--

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</body>
</html>