Fete of Combinatorics and Computer Science Discrete Mathematics and theoretical computer science are closely linked research areas with strong impacts on applications and various other scientific disciplines. Both fields deeply cross fertilize each other. One of the persons who particularly contributed to building bridges between these and many other areas is László Lovász whose outstanding scientific work has defined and shaped many research directions in the past 40 years. A number of friends and colleagues all top authorities in their fields of expertise gathered at the two conferences in August 2008 in Hungary celebrating Lovász 60th birthday. It was a real fete of combinatorics and computer science. Some of these plenary speakers submitted their research or survey papers prior to the conferences. These are included in the volume Building Bridges . The other speakers were able to finish their contribution only later these are collected in the present volume. High Degree Graphs Contain Large Star Factors Iterated Triangle Partitions PageRank and Random Walks on Graphs Solution of Peter Winkler’s Pizza Problem*† Tight Bounds for Embedding Bounded Degree Trees Betti Numbers are Testable* Rigid and Globally Rigid Graphs with Pinned Vertices Noise Sensitivity and Chaos in Social Choice Theory Coloring Uniform Hypergraphs with Small Edge Degrees Extremal Graphs and Multigraphs with Two Weighted Colours Regularity Lemmas for Graphs Edge Coloring Models as Singular Vertex Coloring Models List Total Weighting of Graphs Open Problems.