Certified Euclidean-Residue Minimal-Alignment Switch Decompositions for Three Edge-Disjoint Hamiltonian Cycles in Eisenstein--Jacobi Networks (opens in new tab)

Eisenstein--Jacobi (EJ) networks are degree-six quotient-lattice interconnection networks. For a generator $\alpha=a+b\rho$, let $N=a^2+ab+b^2$ and $d=\gcd(a,b)$. If $d=1$, the three natural unit directions already give three edge-disjoint Hamiltonian cycles. If $d>1$, each unit direction splits into $d$ cycles and the EDHC problem becomes a cycle-splicing problem. Existing non-coprime EJ decompositions prove existence by using a rectangular rep...