Edge Colouring of Cactus Graphs

Edge colouring of an undirected graph G = (V;E) is assigning a colour to each edge e2 E so that any two edges having end-vertex in common have difierent colours. That is, the edge colouring problem asks for assigning colours from a minimum number of colours to edges of a graph such that no two edges with the same colour are incident to the same node. The minimum number of colours required for an edge colouring of G is denoted by ´ 0 (G). A cactus graph is a connected graph in which every block is either an edge or a cycle. In this paper, we colour the edges of a cactus graph with minimum number of colours.