Panpropositionable Hamiltonian graph

Panpropositionable Hamiltonian graph --- панпропозицируемый гамильтонов граф.

A Hamiltonian graph [math]\displaystyle{ G }[/math] is panpropositionable if for any two diffe\-rent vertices [math]\displaystyle{ x }[/math] and [math]\displaystyle{ y }[/math] of [math]\displaystyle{ G }[/math] and any integer [math]\displaystyle{ k }[/math] with [math]\displaystyle{ d_{G}(x,y) \leq k \lt |V(G)|/2 }[/math], there exists a Hamiltonian cycle [math]\displaystyle{ C }[/math] of [math]\displaystyle{ G }[/math] with [math]\displaystyle{ d_{G}(x,y) = k }[/math].