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Edge weights and vertex colours. (English) Zbl 1042.05045
Summary: Can the edges of any non-trivial graph be assigned weights from $$\{1,2,3\}$$ so that adjacent vertices have different sums of incident edge weights?
We give a positive answer when the graph is 3-colourable, or when a finite number of real weights is allowed.

##### MSC:
 05C15 Coloring of graphs and hypergraphs
##### Keywords:
Edge weighting; Vertex colouring
Full Text:
##### References:
 [1] P.N. Balister, E. Györi, J. Lehel, R.H. Schelp, Adjacent vertex distinguishing edge-colorings, to appear. [2] Balister, P.N.; Riordan, O.M.; Schelp, R.H., Vertex-distinguishing edge colorings of graphs, J. graph theory, 42, 95-109, (2003) · Zbl 1008.05067 [3] Erdős, P.; Lovász, L., Problems and results on 3-chromatic hypergraphs and some related questions, (), 609-627 [4] Frieze, A.; Gould, R.J.; Karoński, M.; Pfender, F., On graph irregularity strength, J. graph theory, 41, 2, 120-137, (2002) · Zbl 1016.05045
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