Invited Contributions -- (Un)-Stable Routing in the Internet: A Survey from the Algorithmic Perspective -- Memory Efficient Anonymous Graph Exploration -- Algorithmic Meta Theorems -- Regular Papers -- A Most General Edge Elimination Polynomial -- Approximating the Metric TSP in Linear Time -- The Valve Location Problem in Simple Network Topologies -- A 3/2-Approximation Algorithm for Finding Spanning Trees with Many Leaves in Cubic Graphs -- On the Pseudo-achromatic Number Problem -- Making Role Assignment Feasible: A Polynomial-Time Algorithm for Computing Ecological Colorings -- Faster Exact Bandwidth -- Additive Spanners for Circle Graphs and Polygonal Graphs -- Upward Straight-Line Embeddings of Directed Graphs into Point Sets -- Complexity of the Packing Coloring Problem for Trees -- Characterizations of Restricted Pairs of Planar Graphs Allowing Simultaneous Embedding with Fixed Edges -- A Lower Bound on the Area Requirements of Series-Parallel Graphs -- On Independent Sets and Bicliques in Graphs -- Evaluations of Graph Polynomials -- Parameterized Complexity for Domination Problems on Degenerate Graphs -- An Algorithm for Finding Input-Output Constrained Convex Sets in an Acyclic Digraph -- Cutwidth of Split Graphs, Threshold Graphs, and Proper Interval Graphs -- The Rank-Width of the Square Grid -- Improved Upper Bounds for Partial Vertex Cover -- On the Expressive Power of CNF Formulas of Bounded Tree- and Clique-Width -- Planar Feedback Vertex Set and Face Cover: Combinatorial Bounds and Subexponential Algorithms -- What Is between Chordal and Weakly Chordal Graphs? -- Parameterized Graph Cleaning Problems -- Traffic Grooming in Unidirectional WDM Rings with Bounded Degree Request Graph -- Fast Robber in Planar Graphs -- From a Circular-Arc Model to a Proper Circular-Arc Model -- DigraphDecompositions and Monotonicity in Digraph Searching -- Searching for a Visible, Lazy Fugitive -- A Faster Shortest-Paths Algorithm for Minor-Closed Graph Classes -- Local Construction and Coloring of Spanners of Location Aware Unit Disk Graphs.

This book constitutes the thoroughly refereed post-conference proceedings of the 34th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2008, held in Durham, UK, in June/July 2008. The 30 revised full papers presented together with 3 invited paper were carefully reviewed and selected from 76 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.