Authors:
M. Horňák, J. Hudák
Title:
On the palette index of complete bipartite graphs
Source:
Discussiones Mathematicae Graph Theory
Received 22.03.2016, Revised 20.10.2016, Accepted 15.12.2016, doi: 10.7151/dmgt.2015

Abstract:
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\le5 and pose two conjectures concerning the palette index of complete bipartite graphs.
Keywords:
edge colouring, palette index, bipartite graph

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