Knotted Hamiltonian cycles in spatial embeddings of complete graphs

摘要

We show the complete graph on n vertices contains a knotted Hamiltonian cycle in every spatial embedding, for n 7. Moreover, we show that for n 8, the minimum number of knotted Hamiltonian cycles in every embedding of Kn is at least (n-1)(n-2)...(9)(8). We also prove K8 contains at least 3 knotted Hamiltonian cycles in every spatialembedding.