This is a question taken from some notes, and I do not know how to solve it, nor I know how to start. Can anyone help me?
Prove that $|E| \geq \lfloor \frac{|V|}{2} \rfloor ^2 $ implies the graph $G$ has at least one triangle.
Asked
Active
Viewed 79 times
2
-
@MishaLavrov Great – Apr 14 '18 at 01:16
-
Mantel's theorem, but you've stated it incorrectly. $|E|\gt\left\lfloor\frac{|V|^2}4\right\rfloor$ implies $G=(V,E)$ has a triangle. – bof Apr 14 '18 at 08:43
-
As a counterexample to your erroneous statement of Mantel's theorem, consider a graph with $|V|=3$ and $|E|=2.$ – bof Apr 14 '18 at 08:46