Bipanpositionable graph

Bipanpositionable graph --- бипанпропозицируемый граф.

A bipartite hamiltonian graph [math]\displaystyle{ G }[/math] is bipanpropositionable if for any two different vertices [math]\displaystyle{ x }[/math] and [math]\displaystyle{ y }[/math] of [math]\displaystyle{ G }[/math] and for any integer [math]\displaystyle{ k }[/math] with [math]\displaystyle{ d_{G}(x,y) \leq k \lt |V(G)|/2 }[/math] and [math]\displaystyle{ (k - D_{G}(x,y)) }[/math] is even, there exists a hamiltonian cycle [math]\displaystyle{ C }[/math] of [math]\displaystyle{ G }[/math] such that [math]\displaystyle{ d-{C}(x,y) = k }[/math].