Before revision:  We simulate these two techniques for graphs of various sparsity with the ibmq_manhattan noise model \textit{  and show that the DFS based technique outperforms the edge coloring based technique , which in turn, outperforms the traditional QAOA circuit in terms of reduction in the number of CNOT gates, and hence the probability of error of the circuit.
After revision:  We simulate these two methods for graphs of various sparsity with the ibmq_manhattan noise model \textit{ and show that the DFS based technique outperforms the edge coloring based technique , which in turn, outperforms the traditional QAOA circuit in terms of reduction in the number of CNOT gates, and hence the probability of error of the circuit.