强N_2-局部连通无爪图的Hamilton性

HAMILTONIAN PROPERTY ON STRONG N_2-LOCALLY CONNECTED CLAW-FREE GRAPHS

运用反证法的证明技巧,对任一无爪图G及其圈C,证明了只要C上有一个接触点是强N_2-局部连通的,则C一定不是最长圈.即证明了强N_2-局部连通无爪图是Hamilton图.

It is proved that the cycle C must be not the longest for every claw-free graph G and a cycle in G,if a catchment vertex is strong N2-locally connected vertex ,that is, the strong N2-locally connected claw-free graph is Hamiltonian one.