Gregarious Path Decomposition of Some Graphs

Abstract

Let G be a simple graph and f(v) a positive integer for each vertex v of G. Form G^f by replacing each v by a set F(v) of f(v) vertices, and each edge uv by complete bipartite graph on bipartition (F(u); F(v)). Can we partition G^f into paths of length 2 which are gregarious, that is, meet three di erent F(u)'s?