Vertex-colouring edge-weightings

A weighting w of the edges of a graph G induces a colouring of the vertices of G where the colour of vertex v, denoted c(v), is Sigma(e is an element of v) w(e). We show that the edges of every graph that does not contain a component isomorphic to K-2 can be weighted from the set {1,...,30} such that in the resulting vertex-colouring of G, for every edge (u, v) of G, c(u) not equal c(v).