# Quantum Approximate Optimization Algorithm for $p=1$

I was running instances of $$3$$-regular graphs with small number of vertices on Qiskit, and for $$p=1$$ the algorithm was giving always the exact solution for the MaxCut problem, after optimizing the parameters. I was wondering though, how do we know if a specific graph can't be solved on $$p=1$$ ? Do we know the limits of QAOA for $$p=1$$ in order to decide with certainty that extra layers are required, given the graph?

There are instances where $$p=2,3$$ or $$4$$ might still be not enough. QAOA is an approximate algorithm as the name suggested, so you don't expect it to find the exact answer.