Complete heteroclinic networks derived from graphs consisting of two cycles

The paper gives correct, constructive proofs and sharp counts for the minimal number of added edges via ∆-cliques that capture the full two-dimensional unstable manifolds at distribution nodes. The model reproduces the same piecewise formulas but its proof hinges on a “first–hit sector” argument that misinterprets completeness: it treats the network as a union of one-dimensional planar connections and claims open sectors of the unstable manifold are captured by adding single planar edges. Without creating ∆-cliques at distribution nodes, this does not contain the entire unstable manifold and thus does not prove completeness. Hence the model’s reasoning is flawed even though its final counts match the paper.