Vertex-coloring graphs with 4-edge-weightings
Ralph Keusch

TL;DR
This paper extends the known results on vertex-coloring edge-weightings by proving that graphs without isolated edges can be vertex-colored with weights from {1,2,3,4}, supporting the conjecture for a broader set.
Contribution
It proves that the vertex-coloring edge-weighting conjecture holds when using the weight set {1,2,3,4}, expanding previous results that used smaller sets.
Findings
The conjecture is true for weight set {1,2,3,4}.
Graphs without isolated edges can be properly vertex-colored with these weights.
Supports the broader conjecture for larger weight sets.
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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Taxonomy
TopicsGraph Labeling and Dimension Problems · Nuclear Receptors and Signaling
