Interpolation theorems for a family of spanning subgraphs

Abstract

Let G be a graph with order p, size q and component number ω. For each i between p - ω and q, let script c signi(G) be the family of spanning i-edge subgraphs of G with exactly ω components. For an integer-valued graphical invariant Mathematical bold italic small phi sign, if H → H′ is an adjacent edge transformation (AET) implies \Mathematical bold italic small phi signp(H) - Mathematical bold italic small phi signf(H′)\ ≤ 1, then Mathematical bold italic small phi sign said is to be continuous with respect to AET. Similarly define the continuity of Mathematical bold italic small phi sign with respect to simple edge transformation (SET). Let Mj(Mathematical bold italic small phi sign) and m..