Geometric and Combinatorial Structures on Graphs

Acknowledgments First of all I want to thank my advisor, Stefan Felsner. In lectures and many discussions I learned a lot from him not only about graph theory and combinatorics. He was also willing to share the large and little tricks and insights that make (scientific) working so much easier. During lunches and many coffee breaks I also learned a lot from Stefan about life, the universe, and everything [3] and I appreciate these insights as much as the mathematical ones. proofreading , comments, and technical support. Not only the aforementioned but the whole discrete math group at TU Berlin (including both coffee machines) has provided an outstanding working environment during the last two and a half years. I also enjoyed the two months that I spent with Emo Welzl's group at ETH Zurich very much. Without the financial support of the Studienstiftung des deutschen Volkes and the research training groups " Combinatorics, Geometry, and Computation " and " Methods for Discrete Structures " I would not have been able to conduct the research presented in this thesis. I thank the organizations and the people behind them for making this possible, in particular Gabriele Klink and Elke Pose. Finally I want to express my gratitude to those people who have not been involved in the actual process of writing this thesis. Their main points of contact with this process were my bad moods every once in a while, probably the least pleasant of all ways of being involved in this whole thing. Among these people are of course my folks, in particular my parents, who not only provided superb all inclusive holidays in Saarbrücken. One of the things I appreciate most is how good they were at knowing when " How is your thesis going? " is not the right question to ask. Greta has been equally good at avoiding this question and also at spending relaxing weekends with me that made the final months of working on the thesis much better than I had hoped for. Well... that's it. So long, and thanks for all the coffee! 1

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