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Partial edge drawings of complete graphs

Marko Lalović (2014) Partial edge drawings of complete graphs. Prešeren awards for students.

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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 (Prešeren awards for students)
    Keywords: partial edge drawings, graph theory, planar graphs, analytic geometry
    Number of Pages: 74
    Language of Content: Slovenian
    Mentor / Comentors:
    Name and SurnameIDFunction
    prof. dr. Gašper Fijavž246Mentor
    Link to COBISS: http://www.cobiss.si/scripts/cobiss?command=search&base=51012&select=(ID=1536095427)
    Institution: University of Ljubljana
    Department: Faculty of Computer and Information Science
    Item ID: 3687
    Date Deposited: 19 Dec 2016 10:34
    Last Modified: 09 Feb 2017 13:20
    URI: http://eprints.fri.uni-lj.si/id/eprint/3687

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