Planar Turan number of {C4, C5} (Spring 2024)


One of the central problems in graph theory is to determine the Turan number, that is, the maximum number of edges in an n-vertex graph which does not contain some specified H as a subgraph. In 2016, Dowden initiated the study of Turan-type problems when host graphs are planar, i.e., graphs that can be embedded in the plane. More specifically, the planar Turan number of a graph H, is the maximum number of edges in a planar graph on n vertices which does not contain H as a subgraph.


This research project is centered on a specific scenario: planar graphs that lack both 4-cycles and 5-cycles. Our objective is to delve into this topic by thoroughly examining a prior paper that explores the planar Turan number for the graph C6. We aim to comprehend the methodology employed in that study and then apply it to our own research endeavor. While no advanced tools might be necessary for our proof, a strong foundation in mathematics and mathematical maturity will be desired for this project.



For more information contact Lina Li (linali@iastate.edu)

People:


Pre-requisites: