IMPROVED LOWER BOUND FOR THE NUMBER OF KNOTTED HAMILTONIAN CYCLES IN SPATIAL EMBEDDINGS OF COMPLETE GRAPHS
YOSHIYASU HIRANO · Journal of Knot Theory and Its Ramifications · 2010
We prove that every spatial embedding of the complete graph K8 contains at least 3 knotted Hamiltonian cycles, and that every spatial embedding of Kn contains at least 3(n - 1)(n - 2) ⋯ 8 knotted Hamiltonian cycles, for n > 8.