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.