The binding number of a graph and its circuits

In this paper we prove the following main results:Theorem A. If bind (G)3/2, thenG–u has a Hamiltonian circuit for every vertexu of graphG_i, unlessG belongs either to two classesH₁ andH₂ of graphs or to some smaller order graphs with |V(G)|17.Theorem B. If bind (G)3/2 and the maximum degree (G)>(n–1)/2, |V(G)|=n>17, thenG is pancyclic (i.e., it contains a circuit of every lengthm, 3m|V(G)|).