We present some classes of graphs which satisfy the acyclic edge colouring conjecture which states that any graph can be acyclically edge coloured with at most âˆ† + 2 colours.

A proper colouring of the edges of a graph G is called acyclic if there is no twocoloured cycle in G. The acyclic chromatic index of G, denoted aâ€²(G), is the least number of colours required for anâ€¦ (More)

An acyclic edge colouringof a graph is a proper edge colouring such that there are no bic hromatic cycles. Theacyclic chromatic indexof a graph is the minimum number k such that there is an acyclicâ€¦ (More)

We propose the following problem. For some k â‰¥ 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 edgeâ€¦ (More)

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 numberâ€¦ (More)

The acyclic edge colouring problem is extensively studied in graph theory. The corner-stone of this field is a conjecture of Alon et. al.[1] that aâ€²(G) â‰¤ âˆ†(G) + 2. In that and subsequent work, aâ€²(G)â€¦ (More)