K Intersection Colouring

We propose the following problem. 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 colouring. The minimum number of colours required for such a colouring is the kintersection chromatic index and is denoted χk. Let f be defined by fk(∆) = max G:∆(G)=∆ {χk(G)} We show that fk(∆) = Θ( 2 k ). We also discuss some open problems.