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@PHDTHESIS{Grter:459818,
      author       = {Grüter, Steffen},
      othercontributors = {Guo, Yubao and Triesch, Eberhard},
      title        = {{A}rc pancyclicity in multipartite tournaments {GTECS} –
                      an application in crystallography},
      address      = {Aachen},
      publisher    = {Shaker},
      reportid     = {RWTH-CONV-145386},
      series       = {Berichte aus der Mathematik},
      pages        = {X, 128 S. : Ill., graph. Darst.},
      year         = {2014},
      note         = {Zweitveröffentlicht auf dem Publikationsserver der RWTH
                      Aachen University; Zugl.: Aachen, Techn. Hochsch., Diss.,
                      2014},
      abstract     = {This thesis consists of two parts where the first one
                      represents theoretical results in the field of
                      arc-pancyclicity and connectivity in multipartite
                      tournaments and the second part presents the graph
                      theoretical ideas and algorithms behind the recently
                      developed software GTECS which is a tool for analysing large
                      structures in crystallography. In Chapter 2 of Part I we
                      study t-pancyclic arcs in strong tournaments T for all t =
                      3,...,|V(T)|. In particular, we consider the maximum number
                      of t-pancyclic arcs on a Hamiltonian cycle of T denoted by
                      $h^t(T)$ and the number of all such arcs in T denoted by
                      $p^t(T).$ In this context, we generalise a theorem due to
                      Moon by showing that $h^t(T)$ is lower bounded by t, t =
                      3,...,|V(T)|, for all strong tournaments. Additionally, we
                      characterise all tournaments T with $h^t(T)$ = t, $p^t(T)$ =
                      t, $h^t(T)$ = t+1 and $p^t(T)$ = t+1, t greater or equal 4.
                      In Chapter 3 we present a first result on
                      out-arc-pancyclicity in multipartite tournaments. While for
                      a strong tournament the existence of a vertex whose all
                      out-arcs are pancyclic has been shown, we give different
                      approaches for a corresponding generalisation. Using one of
                      these approaches, we finally present a similar result for
                      2-strong multipartite tournaments and show that it is best
                      possible in general. In Chapter 4 we consider digraphs in
                      general and transfer the concept of tree spanners in
                      connected graphs to connected digraphs by introducing pairs
                      of tree spanners. In this context, we adapt results
                      concerning the existence of special additive (tree) spanners
                      in the class of (alpha, r)-decomposable graphs to the
                      equivalent directed case. Part II of this thesis including
                      the Chapters 5 to 8 starts with an introduction of GTECS,
                      which is the result of an interdisciplinary project of
                      chemists, computer scientists and mathematicians. We show
                      the necessity of such a tool for the analysis of extended
                      crystal structures and introduce the concept of representing
                      such structures by periodic graphs. Depending on this graph
                      class, we introduce various algorithms to simplify the given
                      structure by keeping its topology using for example path- or
                      cycle-contraction. While the main algorithm gives valuable
                      information about the periodicity and the number of
                      components of such a structure, we conclude with a chapter
                      on topological symbols which are important measurements for
                      comparing different structures and show how they are
                      calculated in GTECS.},
      keywords     = {Graphentheorie (SWD) / Kristallographie (SWD)},
      cin          = {110000 / 114510 / 113210},
      ddc          = {510},
      cid          = {$I:(DE-82)110000_20140620$ / $I:(DE-82)114510_20140620$ /
                      $I:(DE-82)113210_20140620$},
      shelfmark    = {05C20 * 05C90},
      typ          = {PUB:(DE-HGF)11 / PUB:(DE-HGF)3},
      urn          = {urn:nbn:de:hbz:82-opus-53017},
      url          = {https://publications.rwth-aachen.de/record/459818},
}