Fault hamiltonicity and fault hamiltonian connectivity of the arrangement graphs

The arrangement graph A/sub n,k/ is a generalization of the star graph. There are some results concerning fault Hamiltonicity and fault Hamiltonian connectivity of the arrangement graph. However, these results are restricted in some particular cases and, thus, are less completed. We improve these results and obtain a stronger and simpler statement. Let n-k/spl ges/2 and F/spl sube/V(A/sub n,k/)/spl cup/E(A/sub n,k/). We prove that A/sub n,k/-F is Hamiltonian if |F|/spl les/k(n-k)-2 and A/sub n,k/-F is Hamiltonian connected if |F|/spl les/k(n-k)-3. These results are optimal.