Abstract
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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Keusch, R. Vertex-Coloring Graphs with 4-Edge-Weightings. Combinatorica 43, 651–658 (2023). https://doi.org/10.1007/s00493-023-00027-6
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DOI: https://doi.org/10.1007/s00493-023-00027-6