The square of a block is Hamiltonian connected

Abstract

AbstractLet 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 M2 to establish the existence of a Hamiltonian path starting at ξ and ending at η in B2. A variant of this trick shows that B2 − ξ has a Hamiltonian circuit