Depth, Crossings and Conflicts in Discrete Geometry

By (author) Marek Sulovsk 'y

Book cover: Depth, Crossings and Conflicts in Discrete Geometry

Extent: 190 pages

Publisher: Logos Verlag Berlin

Subjects: Technical Sciences: Computer Science, Engineering, IT, & Math

Language: English

Paperback (Published)

(March 2012)

ISBN: 9783832531195

5.71 x 8.27 inches

Price: $54.00

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Discrete geometry has been among the fastest growing fields of mathematics in the last decades. One of the most fascinating objects studied in discrete geometry are k-sets. Not only are they extremely difficult to understand but they also play an important role in estimating the running time of several geometric algorithms. This thesis presents developments in three areas related to k-sets. First, it examines the circle containment problem of Urrutia and Neumann-Lara and reveals its relationships to geometric partitioning problems and centre regions. Next, it investigates k-sets in low dimensions and generalises the k-edge crossing identity of Andrzejak et al. to the sphere. Last, it studies conflict-free colourings of geometric hypergraphs and extends many results on this topic to more restrictive list colouring variants.

  • By (author) Marek Sulovsk ‘y

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