Computational Complexity of Generalized Domination: A Complete Dichotomy for Chordal Graphs -- Recognizing Bipartite Tolerance Graphs in Linear Time -- Graph Searching in a Crime Wave -- Monotonicity of Non-deterministic Graph Searching -- Tree-Width and Optimization in Bounded Degree Graphs -- On Restrictions of Balanced 2-Interval Graphs -- Graph Operations Characterizing Rank-Width and Balanced Graph Expressions -- The Clique-Width of Tree-Power and Leaf-Power Graphs -- NLC-2 Graph Recognition and Isomorphism -- A Characterisation of the Minimal Triangulations of Permutation Graphs -- The 3-Steiner Root Problem -- On Finding Graph Clusterings with Maximum Modularity -- On Minimum Area Planar Upward Drawings of Directed Trees and Other Families of Directed Acyclic Graphs -- A Very Practical Algorithm for the Two-Paths Problem in 3-Connected Planar Graphs -- Approximation Algorithms for Geometric Intersection Graphs -- An Equivalent Version of the Caccetta-Häggkvist Conjecture in an Online Load Balancing Problem -- Mixing 3-Colourings in Bipartite Graphs -- Minimum-Weight Cycle Covers and Their Approximability -- On the Number of ?-Orientations -- Complexity and Approximation Results for the Connected Vertex Cover Problem -- Segmenting Strings Homogeneously Via Trees -- Characterisations and Linear-Time Recognition of Probe Cographs -- Recognition of Polygon-Circle Graphs and Graphs of Interval Filaments Is NP-Complete -- Proper Helly Circular-Arc Graphs -- Pathwidth of Circular-Arc Graphs -- Characterization and Recognition of Digraphs of Bounded Kelly-width -- How to Use Planarity Efficiently: New Tree-Decomposition Based Algorithms -- Obtaining a Planar Graph by Vertex Deletion -- Mixed Search Number and Linear-Width of Interval and Split Graphs -- Lower Bounds for Three Algorithms for the Transversal Hypergraph Generation -- The Complexity of Bottleneck Labeled Graph Problems.

This book constitutes the thoroughly refereed post-proceedings of the 33rd International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2007, held in Dornburg, Germany, in June 2007. The 30 revised full papers presented together with 1 invited paper were carefully selected from 99 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 graph and network algorithms and their complexity, graph grammars and graph rewriting systems, graph-based modeling, graph-drawing and layout, diagram methods, and support of these concepts by suitable implementations.