@phdthesis{Kryven2022,
  author    = {Kryven, Myroslav},
  title     = {Optimizing Crossings in Circular-Arc Drawings and Circular Layouts},
  isbn      = {978-3-95826-174-7},
  doi       = {10.25972/WUP-978-3-95826-175-4},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-245960},
  school      = {Universit{\"a}t W{\"u}rzburg},
  pages     = {viii, 129},
  year      = {2022},
  abstract  = {A graph is an abstract network that represents a set of objects, called vertices, and relations between these objects, called edges. Graphs can model various networks. For example, a social network where the vertices correspond to users of the network and the edges represent relations between the users. To better see the structure of a graph it is helpful to visualize it. The research field of visualizing graphs is called Graph Drawing. A standard visualization is a node-link diagram in the Euclidean plane. In such a representation the vertices are drawn as points in the plane and edges are drawn as Jordan curves between every two vertices connected by an edge. Edge crossings decrease the readability of a drawing, therefore, Crossing Optimization is a fundamental problem in Graph Drawing. Graphs that can be drawn with few crossings are called beyond-planar graphs. The topic that deals with definition and analysis of beyond-planar graphs is called Beyond Planarity and it is an important and relatively new research area in Graph Drawing. In general, beyond planar graphs posses drawings where edge crossings are restricted in some way. For example, the number of crossings may be bounded by a constant independent of the size of the graph. Crossings can also be restricted locally by, for example, restricting the number of crossings per edge, restricting the number of pairwise crossing edges, or bounding the crossing angle of two edges in the drawing from below. This PhD thesis defines and analyses beyond-planar graph classes that arise from such local restrictions on edge crossings.},
  subject      = {Graphenzeichnen},
  language  = {en}
}