This book constitutes the thoroughly refereed post-workshop proceedings of the 24th International Workshop on Graph-Theoretic Concepts in Computer Science, WG'98, held in Smolenice Castle, Slovak Republic, in June 1998. The 30 revised full papers presented were carefully selected from a total of 61 submissions. The papers provide a wealth of new results for various classes of graphs, graph computations, graph algorithms and graph-theoretic applications in computer science.