Edge-oblique polyhedral graphs Original Research Article

Let G=G(V,E,F) be a polyhedral graph with vertex set V, edge set E and face set F. e=(x,y;α,β)∈E(G) denotes an edge incident with the two vertices x,y∈V(G), d(x)⩽d(y) and incident with the two faces α,β∈F(G), d(α)⩽d(β). [K=d(x),L=d(y);M=d(α), N=d(β)] is the type of e=(x,y;α,β). A graph which contains no two edges of a common edge-type is called edge-oblique and if it contains at most z edges of each type it is called z-edge-oblique. In this work we shall prove, that there is only a finite number of edge-oblique and z-edge-oblique graphs. For the first case some bounds for the maximum degree and the number of edges are given.