Vertex-Colouring Edge-Weightings. - Addario-Berry, L; Dalal, K; McDiarmid, C; Reed, B; Thomason, A (2007)
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 cv , is Σe∋vw(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, cu≠cv . © 2007 Springer-Verlag Berlin Heidelberg.