IMPROVED LOWER BOUND FOR THE NUMBER OF KNOTTED HAMILTONIAN CYCLES IN SPATIAL EMBEDDINGS OF COMPLETE GRAPHS

We prove that every spatial embedding of the complete graph K₈ contains at least 3 knotted Hamiltonian cycles, and that every spatial embedding of K_n contains at least 3(n - 1)(n - 2) ⋯ 8 knotted Hamiltonian cycles, for n > 8.