Show that in every graph with 6 vertices and 10 edges there are two vertices of degree 4.
So I know any graph o must have two of the same degree. But I'm not sure if I can apply this here? I feel like I have too many unknowns to apply that proof here?
The statement is not correct. The degree sequence of the graph could be $5, 3,3,3,3,3$ (imagine a wheel with $5$ spokes coming out from a central point).