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People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.This thesis would never appear without the endless support of some people. I am glad to name them here. First of all, many thanks go to my enormously patient supervisor, Alexander Grigoriev. He was always full of enthusiasm and new ideas about any project.Part of the research was made in close cooperation with André Berger and Bert Marchal. I am very grateful for the knowledge, ideas and precision they brought into the thesis. My special thanks go to Bert for his patience and for always being there for me.The unconditional support of my parents led me from the secondary school to this doctoral thesis. Without their understanding and help I would never proceeded so far. Thank you, mom and dad.Special thanks to my beloved roommate Bas, for charts and the guidance through the Dutch culture and humor. His regular jokes and shiny smiles made rainy days much brighter. He was not the only one who lightened my life during these years. Without mentioning their names I thank all the friends and colleagues from the university, who made my life in Maastricht a very enjoyable and precious time.A lot of thanks go to Karin and Haydeé for their help with all the paper work. These pretty ladies make the atmosphere in the department pleasant and relaxing.I thank Rudolf Müller, Jean Cardinal and Ralf Peeters for refereeing the thesis and for all the useful comments they provided to make the text more clear and readable.The research that forms the basis of this thesis was conducted from 2008 to 2011 at the Quantitative Economics department; it was funded by the department and by Maastricht Research School of Economics of Technology and Organizations (ME-TEOR). This support is gratefully acknowledged.

In this note we consider the following problem: Given a graph [Formula: see text] and a subgraph [Formula: see text], what is the smallest subset [Formula: see text] of edges in [Formula: see text] that needs to be deleted from the graph to make it [Formula: see text]-free? Several algorithmic results are presented. First, using the general framework of Courcelle [9], we show that, for a fixed subgraph [Formula: see text], the problem can be solved in linear time on graphs of bounded treewidth. It is known that the constant hidden in the big-O notation of Courcelle algorithm is big which makes the approach impractical. Thus, we present two explicit linear time dynamic programming algorithms on graphs of bounded treewidth for restricted settings of the problem with reasonable constants. Third, using the linear time algorithm for graphs of bounded treewidth, we design a Baker's type polynomial time approximation scheme for the problem on planar graphs.