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  <doc>
    <id>793</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2004-05-28</completedDate>
    <publishedDate>2004-05-28</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Holes, Antiholes and Maximal Cliques in a Railway Model for a Single Track</title>
    <abstract language="eng">We present a graph theoretical model for scheduling trains on a single unidirectional track between two stations. The set of departures of all possible train types at all possible (discrete) points of time is turned into an undirected graph $\Gneu$ by joining two nodes if the corresponding departures are in conflict. This graph $\Gneu$ has no odd antiholes and no $k$-holes for any integer $k\geq 5$. In particular, any finite, node induced subgraph of $\Gneu$ is perfect. For any integer $r\geq 2$ we construct minimal headways for $r$ train types so that the resulting graph $\Gneu$ has $2r$-antiholes and $4$-holes at the same time. Hence, $\Gneu$ is neither a chordal graph nor the complement of a chordal graph, in general. At the end we analyse the maximal cliques in $G$.</abstract>
    <identifier type="serial">04-18</identifier>
    <identifier type="opus3-id">794</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-7939</identifier>
    <author>Sascha Lukac</author>
    <series>
      <title>ZIB-Report</title>
      <number>04-18</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>perfect graphs</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>holes</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>anti holes</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cliques</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>railway</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="05C17">Perfect graphs</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/793/ZR-04-18.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/793/ZR-04-18.pdf</file>
  </doc>
</export-example>
