This book constitutes the thoroughly refereed post-conference proceedings of the 35th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2009, held in Montpellier, France, in June 2009. The 28 revised full papers presented together with two invited papers were Carefully Reviewed and selected from 69 submissions. The papers feature original results on all aspects of graph-theoretic concepts in Computer Science, e.g. structural graph theory, sequential, parallel, and distributed g

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