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Depth, Crossings and Conflicts in Discrete Geometry
Marek Sulovsk 'yMarek Sulovský
出版Logos Verlag Berlin GmbH, 2012
主題Mathematics / GeneralMathematics / Geometry / General
ISBN383253119X9783832531195
URLhttp://books.google.com.hk/books?id=0Q9mbXCQRyoC&hl=&source=gbs_api
EBookSAMPLE
註釋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.