This book constitutes the thoroughly refereed post-proceedings of the 32nd International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2006, held in Bergen, Norway in June 2006. The 30 revised full papers presented together with 1 invited paper were carefully selected from 91 submissions. The papers address all aspects of graph-theoretic concepts in computer science such as structural graph theory, sequential, parallel, and distributed graph and network algorithms and their complexity, graph grammars and graph rewriting systems, graph-based modeling, graph-drawing and layout, diagram methods, and graph-theoretical applications in various fields.