Geodesic
On k-intersection edge colourings
Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 2, pp. 411-418

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We propose the following problem. For some k ≥ 1, a graph G is to be properly edge coloured such that any two adjacent vertices share at most k colours. We call this the k-intersection edge colouring. The minimum number of colours sufficient to guarantee such a colouring is the k-intersection chromatic index and is denoted χ'ₖ(G). Let fₖ be defined by
Keywords: graph theory, k-intersection edge colouring, probabilistic method 
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Muthu, Rahul; Narayanan, N.; Subramanian, C. On k-intersection edge colourings. Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 2, pp. 411-418. http://geodesic.mathdoc.fr/item/DMGT_2009_29_2_a14/