A note on hamiltonicity of generalized net-free graphs of large diameter Original Research Article

A generalized (i,j,k)-net Ni,j,k is the graph obtained by identifying each of the vertices of a triangle with an endvertex of one of three vertex-disjoint paths of lengths i,j,k. We prove that every 2-connected claw-free N1,2,j-free graph of diameter at least max{7,2j} (j⩾2) is hamiltonian.