This book constitutes the thoroughly refereed postproceedings of the 29th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2003, held in Elspeet, The Netherlands in June 2003.The 30 revised full papers presented together with 2 invited papers were carefully reviewed, improved, and selected from 78 submissions. The papers present a wealth of new results for various classes of graphs, graph computations, graph algorithms, and graph-theoretical applications in various felds.