Graph modification problems related to graph classes

i Acknowledgements The first person I need to thank is my supervisor Pinar Heggernes. Without her guidance, encouragement and scolding from time to time, this work would not exist. Thank you for taking me as your student, teaching me so much and believing in me from the very start. I have never told you how much this meant to me, but I hope this thesis can make up for at least some of it. These three years gave me the opportunity to fulfill many of my dreams, and for this I will always be thankful to you. Another person to whom I owe a lot for his unconditional help, even when he hardly knew me, is Marc Bezem. Your support has been critical in many occasions, including when I had to decide whether to apply for this PhD. Thank you for convincing me to do it, or I would have regretted it forever. I would like to thank also all my co-Tuy for making the two months at Rostock University extremely enjoyable for me and my family. If my PhD has been such a great experience, it is due mostly to all my colleagues at the Algorithms Group. I would like to thank in particular Alexey for all the fun time we spent together fishing, hiking, drinking or talking just about anything. All of this before we both got married of course.... Joanna, thanks for never letting things get boring, and Morten, one day we will catch that giant cod, I promise. A special thank to Yngve, who is always there with a reasonable answer to practically any question one could think about. Maybe too many stupid questions are also the reason why he moved out of our office, but thanks to this I could get a very thoughtful new office mate. Daniel thanks for always making sure that I do not work too much, and Saket, thank you for keeping Daniel out of the office. Serge, Rodica and Daniel, thanks to you too for being around and help me whenever I needed it. I also want to thank my parents for always supporting my choices and making sure that I have everything I need, despite the distance that separates us. Finally I want to dedicate this work to my lovely wife Hilde and our beautiful son Alessandro. Hilde, thanks for taking care of Alessandro on your own while I …