Title: Topics in Extremal Graph Theory
MATH 3912 (Junior Seminar) presentation
by Cristian Aldea
Brandon Cruz
Michael Gaccione
Oksana Jablonsky
Danielle Shelton
Abstract
Some results in graph theory state: if a graph G is of fixed order n and has at
least size f(n) ( # of edges), then G contains a particular subgraph , or G
has some kind of property. Determining the sharp bounds and resulting
extremal graphs is an area of graph theory called extremal graph theory.
We extend some existing extremal results for simple graphs (On the
extensions of Turan’s theorem) to multigraphs. Also, Ramsey Theory in the
context of multigraphs is introduced.