ON THE HAMILTONIAN INDEX OF A GRAPH

It was claimed by Gould (1981) that if G is a connected graph of order at least 3 such that no bridge is incident to a vertex of degree 2 an d no path contains three or more consecutive vertices of degree 2, the n L2(G) is hamiltonian. By H.-J. Lai (1988), this was proved to be fal se. Necessary and sufficient conditions for corresponding counterexamp les were also displayed. However, this characterization is not complet e because some counterexamples were overlooked as is proved in this no te. Furthermore, a counterexample to a theorem of Chartrand and Wall ( 1973) about hamiltonian index of graphs with hamiltonian cyclic blocks was exhibited by Lai (1988). Here an alternative version of this theo rem is presented.