Geodesic
On the Palette Index of Complete Bipartite Graphs
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 2, pp. 463-476 Cet article a éte moissonné depuis la source Library of Science

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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/

[1] S. Bonvicini and G. Mazzuoccolo, Edge-colorings of 4- regular graphs with the minimum number of palettes, Graphs Combin. 32 (2016) 1293–1311. doi:10.1007/s00373-015-1658-7

[2] M. Horňák, R. Kalinowski, M.Meszka andM.Woźniak, Minimum number of palettes in edge colorings, Graphs Combin. 30 (2014) 619–626. doi:10.1007/s00373-013-1298-8

[3] C.C. Lindner, M. Meszka and A. Rosa, Palettes in block colourings of designs, Australas. J. Combin. 56 (2013) 235–243.