On the complexity of vertex-coloring edge-weightings

Andrzej Dudek, David Wajc '
2011 Discrete Mathematics and Theoretical Computer Science DMTCS   unpublished
Given a graph G = (V, E) and a weight function w : E → R, a coloring of vertices of G, induced by w, is defined by χw(v) = ev w(e) for all v ∈ V. In this paper, we show that determining whether a particular graph has a weighting of the edges from {1, 2} that induces a proper vertex coloring is NP-complete.