A Best Possible Result for the Square of a 2-Block to be Hamiltonian

Abstract

It is shown that for any choice of four different vertices x 1 , ..., x 4 in a 2-block G of order p > 3, there is a hamiltonian cycle in G 2 containing four different edges x i y i of E(G) for certain vertices y i , i = 1, 2, 3, 4. This result is best possible.