Universal maximal packing functions of graphs Original Research Article

A packing function of a graph G = (V, E) is a function ƒ: V → [0,1] such that for each v ϵ V, Σu ϵ N [v] ƒ (u) ⩽ 1 (where N [v] denotes the closed neighbourhood of vertex v). We consider the existence of universal maximal packing functions, i.e. maximal packing functions (MPFs) whose convex combinations with all other MPFs are themselves MPFs.