Cai, Leizhen2024-08-132024-08-1319881988https://hdl.handle.net/1828/17396Edge colouring a graph is a classic algorithmi,; graph problem which has many applications. The problem of determining the chnmatic index is, in general, NP­-complete. This thesis investigates the computational complexity of edge colouring restricted graphs. Previous work has established that the chromatic index problem restricted to k­-regular graphs for any fixed k-3 remains NP-complete, whereas the problem restricted to bipartite graphs and partial k-trees for fixed k is in P. We show that the chromatic index problem restricted to comparability graphs, perfect graphs, line graphs, claw-free graphs, triangle-free graphs and some others remains NP-complete. We present linear time optimal edge colouring algorithms for complete graphs, the liPe graphs of trees and the ln 1e graphs of unicyclic graphs. We also present a linear time approximation algorithm, which uses at most four colours, for cubic graphs, and an O (1.682 IV I) algorithm for determining the chromatic index of any cubic graph.89 pagesAvailable to the World Wide WebThesis