Geodesic
On the Palette Index of Complete Bipartite Graphs
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 2, pp. 463-476

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The palette of a vertex x of a graph G determined by a proper edge colouring φ of G is the set φ(xy) : xy ∈ E(G) and the diversity of φ is the number of different palettes determined by φ. The palette index of G is the minimum of diversities of φ taken over all proper edge colourings φ of G. In the article we determine the palette index of Km,n for m ≤ 5 and pose two conjectures concerning the palette index of complete bipartite graphs.
Keywords: edge colouring, palette index, bipartite graph 
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Horňák, Mirko; Hudák, Juraj. On the Palette Index of Complete Bipartite Graphs. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 2, pp. 463-476. http://geodesic.mathdoc.fr/item/DMGT_2018_38_2_a9/