ON k-INTERSECTION EDGE COLOURINGS.

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 fk(Δ) = (These character(s) cannot be represented in ASCII text). We show that (These character(s) cannot be represented in ASCII text). We also discuss some open problems. [ABSTRACT FROM AUTHOR]