Universal maximal packing functions of graphs (Q1126177)

A nonnegative function \(f\) defined on the vertex set of a graph \(G\) is a packing function (PF) if for each vertex \(v\) the sum of the values of \(f\) over the closed neighbourhood of \(v\) is at most 1; such a function \(f\) is a maximal packing function (MPF) if it no longer satisfies the definition of a PF when its value is increased for any vertex. The authors consider the existence of MPFs with the property that their convex combinations with all other MPFs are themselves MPFs.