Problem 11. (10 points) Use induction to prove that any graph with n3 vertices and n edges has a cycle. Problem 12. (10 points) Use induction to prove that i=1N(2i1)=N2. Problem 13. (10 points) Prove if n7 then 2(n7)2+4lg(n2)+3nlg(n2)+n/210n2 (you can use basic, well known mathematical facts, but should show any non-obvious step)