  Using algebraic transformations and equivalent reformulations we derive a
number of new results from some earlier ones (by the author) in more accepted
terms closely related to well-known conjectures of Bondy and Jung including a
number of classical results in hamiltonian graph theory (due to Dirac, Ore,
Nash-Williams, Bondy, Jung and so on) as special cases. A number of extended
and strengthened versions of these conjectures are proposed.
