Invited Lectures -- Hypertree Decompositions: Structure, Algorithms, and Applications -- Combinatorial Search on Graphs Motivated by Bioinformatics Applications: A Brief Survey -- Regular Papers -- Domination Search on Graphs with Low Dominating-Target-Number -- Fully Dynamic Algorithm for Recognition and Modular Decomposition of Permutation Graphs -- Approximating Rank-Width and Clique-Width Quickly -- Computing the Tutte Polynomial on Graphs of Bounded Clique-Width -- Minimizing NLC-Width is NP-Complete -- Channel Assignment and Improper Choosability of Graphs -- Computing Treewidth and Minimum Fill-In for Permutation Graphs in Linear Time -- Roman Domination over Some Graph Classes -- Algorithms for Comparability of Matrices in Partial Orders Imposed by Graph Homomorphisms -- Network Discovery and Verification -- Complete Graph Drawings Up to Triangle Mutations -- Collective Tree 1-Spanners for Interval Graphs -- On Stable Cutsets in Claw-Free Graphs and Planar Graphs -- Induced Subgraphs of Bounded Degree and Bounded Treewidth -- Optimal Broadcast Domination of Arbitrary Graphs in Polynomial Time -- Ultimate Generalizations of LexBFS and LEX M -- Adding an Edge in a Cograph -- The Computational Complexity of Delay Management -- Acyclic Choosability of Graphs with Small Maximum Degree -- Generating Colored Trees -- Optimal Hypergraph Tree-Realization -- Fixed-Parameter Algorithms for Protein Similarity Search Under mRNA Structure Constraints -- On the Fixed-Parameter Enumerability of Cluster Editing -- Locally Consistent Constraint Satisfaction Problems with Binary Constraints -- On Randomized Broadcasting in Star Graphs -- Finding Disjoint Paths on Directed Acyclic Graphs -- Approximation Algorithms for the Bi-criteria Weighted max-cut Problem -- Approximation Algorithms for the Weighted Independent Set Problem -- Approximation Algorithms for Unit Disk Graphs -- Computation of Chromatic Polynomials Using Triangulations and Clique Trees -- Computing Branchwidth Via Efficient Triangulations and Blocks -- Algorithms Based on the Treewidth of Sparse Graphs -- Extending the Tractability Border for Closest Leaf Powers -- Bounding the Misclassification Error in Spectral Partitioning in the Planted Partition Model -- Algebraic Operations on PQ Trees and Modular Decomposition Trees -- Linear-Time Counting Algorithms for Independent Sets in Chordal Graphs -- Faster Dynamic Algorithms for Chordal Graphs, and an Application to Phylogeny -- Recognizing HHDS-Free Graphs.

This book constitutes the thoroughly refereed post-proceedings of the 31st International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2005, held in Metz, France in June 2005. The 38 revised full papers presented together with 2 invited papers were carefully selected from 125 submissions. The papers provide a wealth of new results for various classes of graphs, graph computations, graph algorithms, and graph-theoretical applications in various fields. The workshop aims at uniting theory and practice by demonstrating how graph-theoretic concepts can be applied to various areas in Computer Science, or by extracting new problems from applications. The goal is to present recent research results and to identify and explore directions of future research.