The square of a block is Hamiltonian connected

Abstract Let B be a block (finite connected graph without cut-vertices) with at least four vertices and ξ, η be distinct vertices of B . We construct a new block M = M ( B , ξ , η ) containing five copies of B , and use the existence of a Hamiltonian circuit in M 2 to establish the existence of a Hamiltonian path starting at ξ and ending at η in B 2 . A variant of this trick shows that B 2 − ξ has a Hamiltonian circuit.