Nika Salia: Extremal problems in planar graphs

Description of video

Date: 4/23/20
Speaker :Salia Nika


    This will be a very special survey type  talk, where authors
    will attempt to popularise a set of old forgotten problems.  We will
    survey our fresh results and give quite a few delicate problems for
    further investigation. Our planar project was inspired by an old result
    of  Hakimi and Schmeichel. In 1979, they considered the problem of
    maximizing the number of cycles of a given length in an n-vertex
    planar graph.  They precisely determined the maximum number of triangles
    and 4-cycles and presented a conjecture for the maximum number of
    pentagons. We confirmed their conjecture and characterized the
    n-vertex, planar graphs with the maximum number of pentagons. Since
    then we got a number of different results about induced pentagons, and
    psaths of length 3 and 4: arXiv: 1909.13532, 1909.13539, 2002.04579,

    Joint Works With Debarun Ghosh, Ervin Győri, Oliver Janzer, Ryan R.
    Martin, Addisu Paulos, Casey Tompkins, Chuanqi Xiao, Oscar Zamora