This book constitutes the thoroughly refereed post-conference proceedings of the 36th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2010, held in Zar s, Crete, Greece, in June 2010. The 28 revised full papers presented together with two invited papers were carefully reviewed and selected from 94 initial submissions. The papers feature original results on all aspects of graph-theoretic concepts in Computer Science, e.g. structural graph theory, sequential, parallel, randomized, parameterized, and distributed graph and network algorithms and their complexity, graph grammars and graph rewriting systems, graph-based modeling, graph-drawing and layout, random graphs, diagram methods, and support of these concepts by suitable implementations - as well as applications of graph-theoretic concepts in Computer Science.