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Vertex-Coloring Graphs with 4-Edge-Weightings

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An edge-weighting of a graph is called vertex-coloring if the weighted degrees yield a proper vertex coloring of the graph. It is conjectured that for every graph without isolated edge, a vertex-coloring edge-weighting with the set \(\{1,2,3\}\) exists. In this note, we show that the statement is true for the weight set \(\{1,2,3,4\}\).

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Correspondence to Ralph Keusch.

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Keusch, R. Vertex-Coloring Graphs with 4-Edge-Weightings. Combinatorica 43, 651–658 (2023).

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