Oblique graph

Oblique graph --- скошенный граф.

A [math]\displaystyle{ k }[/math]-gon [math]\displaystyle{ \alpha }[/math] of a polyhedral graph [math]\displaystyle{ G = (V,E,F) }[/math] with the face set [math]\displaystyle{ F }[/math] is of type [math]\displaystyle{ \langle b_{1}, \ldots, b_{k}\rangle }[/math] if the vertices incident with [math]\displaystyle{ \alpha }[/math] in a cyclic order have degrees [math]\displaystyle{ b_{1}, \ldots, b_{k} }[/math] and [math]\displaystyle{ \langle b_{1}, \ldots, b_{k} \rangle }[/math] is the lexicographic minimum of all such sequences available for [math]\displaystyle{ \alpha }[/math]. A polyhedral graph [math]\displaystyle{ G }[/math] is oblique if it has no two faces of the same type.

[math]\displaystyle{ G }[/math] is superoblique if both [math]\displaystyle{ G }[/math] and its dual [math]\displaystyle{ G^{\ast} }[/math] are oblique and they have no common face type. Let [math]\displaystyle{ z }[/math] be any given natural number. A polyhedral graph [math]\displaystyle{ G }[/math] is [math]\displaystyle{ z }[/math]-oblique if [math]\displaystyle{ F(G) }[/math] contains at most [math]\displaystyle{ z }[/math] faces of the same type for any type of faces. Obviously, a 1-oblique graph is oblique and vice versa.