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This 2007 volume contains survey articles based on the invited lectures given at the Twenty-first British Combinatorial Conference, held in July 2007 at the University of Reading. This biennial conference is a well-established international event and the articles are of the high quality that befits the event. By its nature this volume provides an overview of current research activity in several areas of combinatorics, ranging from graph theory to current applications of combinatorial mathematics, including efficient approximability of NP-hard optimization problems and cryptographic key...