Aspects of the invention relate to techniques of layout decomposition for triple patterning lithography. Data of a coloring graph are derived from layout data for a layout design. The coloring graph is simplified through graph reduction and graph partitioning processes. The graph partitioning process comprises separating biconnected components. The graph partitioning process may further comprise separating subgraphs connected by one or two edges. Based on the simplified coloring graph, the layout design is decomposed to generate decomposition information. The decomposition process may comprise applying a heuristic method for coloring if needed. The decomposition information may comprise information of one or more layout regions that cannot be decomposed.