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Vertex-coloring edge-weightings: towards the 1-2-3-conjecture. (English) Zbl 1209.05087
Summary: A weighting of the edges of a graph is called vertex-coloring if the weighted degrees of the vertices yield a proper coloring of the graph. In this paper we show that such a weighting is possible from the weight set $$\{1,2,3,4,5\}$$ for all graphs not containing components with exactly 2 vertices.

##### MSC:
 05C15 Coloring of graphs and hypergraphs 05C07 Vertex degrees
##### Keywords:
irregular graph labellings
Full Text:
##### References:
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