Oscar Zamora Luna: A generalized Turán problem on Planar Graphs: The Maximum Number of Pentagons in a Planar Graph

Hakimi and Schmeichel considered the problem of maximizing the number of cycles of a given

length in an $n$-vertex planar graph. They determined this number exactly for triangles and

4-cycles and conjectured the solution to the problem for 5-cycles. We confirm their conjecture.

This is joint work with Ervin Gyori, Adissu Pauloa, Nika Salia and Casey Tompkins