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Partial edge drawings of complete graphs

Marko Lalović (2014) Partial edge drawings of complete graphs. EngD thesis.

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    Partial edge drawing of a graph is a rectilinear drawing in which a middle portion of an edge is removed from the drawing. In addition, we require that the drawing is without edge crossings. Currently, the best estimate claims that there is no partial edge drawing of the complete graph on 241 or more points. In this work we improve the estimate by a factor of more than two. We show that it is not possible to draw a partial edge drawing of the complete graph on 102 or more points. The main ideas are two. On the one hand, we use a different division of the plane on which the points of the graph are located. Instead of coordinate division of the plane, we use the areas along the rays from pre-selected points of the drawing. On the other hand, we analyze the whole drawing of the graph by the location of three, sometimes even four, points of the drawing and not only two points as in the previous estimates.

    Item Type: Thesis (EngD thesis)
    Keywords: partial edge drawings, graph theory, planar graphs, analytic geometry
    Number of Pages: 74
    Language of Content: Slovenian
    Mentor / Comentors:
    Name and SurnameIDFunction
    izr. prof. dr. Gašper Fijavž246Mentor
    Link to COBISS: http://www.cobiss.si/scripts/cobiss?command=search&base=50070&select=(ID=00010785108)
    Institution: University of Ljubljana
    Department: Faculty of Computer and Information Science
    Item ID: 2630
    Date Deposited: 02 Sep 2014 16:52
    Last Modified: 30 Sep 2014 13:59
    URI: http://eprints.fri.uni-lj.si/id/eprint/2630

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