Let G be a graph of order n and 3≤ t≤ n/4 be an integer. Recently, Kaneko and Yoshimoto
[J Combin Theory Ser B 81 (1)(2001), 100–109] provided a sharp δ (G) condition such that
for any set X of t vertices, G contains a hamiltonian cycle H so that the distance along H
between any two vertices of X is at least n/2t. In this article, minimum degree and
connectivity conditions are determined such that for any graph G of sufficiently large order n
and for any set of t vertices X⊆ V (G), there is a hamiltonian cycle H so that the distance …

… In this paper, minimum degree and connectivity conditions are determined such that for
any graph G of sufficiently large order n and for any set of t vertices X ⊆ V (G), there is a
hamiltonian cycle H so that the distance along H between any two consecutive vertices of X
is approximately n … . Furthermore, we determine the δ threshold for any t chosen vertices
to be appear on a hamiltonian cycle H in a prescribed order, with approximately
predetermined distances along H between consecutive chosen vertices. … Our results show …