Invited Talks -- Algorithmic Barriers from Phase Transitions in Graphs -- Algorithmic Graph Minors and Bidimensionality -- Regular Talks -- Complexity Results for the Spanning Tree Congestion Problem -- max-cut and Containment Relations in Graphs -- The Longest Path Problem is Polynomial on Cocomparability Graphs -- Colorings with Few Colors: Counting, Enumeration and Combinatorial Bounds -- On Stable Matchings and Flows -- Narrowing Down the Gap on the Complexity of Coloring P k -Free Graphs -- Computing the Cutwidth of Bipartite Permutation Graphs in Linear Time -- Solving Capacitated Dominating Set by Using Covering by Subsets and Maximum Matching -- Efficient Algorithms for Eulerian Extension -- On the Small Cycle Transversal of Planar Graphs -- Milling a Graph with Turn Costs: A Parameterized Complexity Perspective -- Graphs that Admit Right Angle Crossing Drawings -- Kernelization Hardness of Connectivity Problems in d-Degenerate Graphs -- On the Boolean-Width of a Graph: Structure and Applications -- Generalized Graph Clustering: Recognizing (p,q)-Cluster Graphs -- Colouring Vertices of Triangle-Free Graphs -- A Quartic Kernel for Pathwidth-One Vertex Deletion -- Network Exploration by Silent and Oblivious Robots -- Uniform Sampling of Digraphs with a Fixed Degree Sequence -- Measuring Indifference: Unit Interval Vertex Deletion -- Parameterized Complexity of the Arc-Preserving Subsequence Problem -- From Path Graphs to Directed Path Graphs -- Connections between Theta-Graphs, Delaunay Triangulations, and Orthogonal Surfaces -- Efficient Broadcasting in Random Power Law Networks -- Graphs with Large Obstacle Numbers -- The Complexity of Vertex Coloring Problems in Uniform Hypergraphs with High Degree -- The Number of Bits Needed to Represent a Unit Disk Graph -- Lattices and Maximum Flow Algorithms in Planar Graphs.

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 Zarós, 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.