<?xml version="1.0" encoding="utf-8"?>
<rss version="2.0">
  <channel>
    <title>OPUS 4 Latest Documents RSS Feed</title>
    <description>Latest documents</description>
    <link>http://opus4.kobv.de/opus4-ubbayreuth/index/index/</link>
    <pubDate>Tue, 12 Jul 2005 14:56:57 +0100</pubDate>
    <lastBuildDate>Tue, 12 Jul 2005 14:56:57 +0100</lastBuildDate>
    <item>
      <title>A note on Erdös-Diophantine graphs and Diophantine carpets</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/177</link>
      <description>A Diophantine figure is a set of points on the integer grid $\mathbb{Z}^{2}$ where all mutual Euclidean distances are integers. We also speak of Diophantine graphs. The vertices are points in $\mathbb{Z}^{2}$ (the coordinates)and the edges are labeled with the distance between the two adjacent vertices, which is integral. In this language a Diophantine figure is a complete Diophantine graph. Two Diophantine graphs are equivalent if they only differ by translation or rotation of vertices. Due to a famous theorem of Erdös and Anning there are complete Diophantine graphs which are not contained in larger ones. We call them Erdös-Diophantine graphs. A special class of Diophantine graphs are Diophantine carpets. These are planar triangulations of a subset of the integer grid. We give an effective construction for Erdös-Diophantine graphs and characterize the chromatic number of Diophantine carpets.</description>
      <author>Axel Kohnert; Sascha Kurz</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/177</guid>
      <pubDate>Wed, 07 Dec 2005 14:56:57 +0100</pubDate>
    </item>
  </channel>
</rss>
