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 management. The authors are some of the world's foremost researchers in their fields, and here they summarize existing results, and give a unique preview of work currently being written up. The book provides a valuable survey of the state of knowledge in combinatorics. It will be useful to research workers and advanced graduate students, primarily in mathematics but also in computer science, statistics and engineering.
• Contains survey articles based on the invited lectures given at the Twenty-first British Combinatorial Conference, a well-established international event • Authors are some of the world's foremost researchers in their fields and their survey articles cover topics ranging from graph theory to current applications of combinatorial mathematics • The volume provides a valuable summary of existing results and a unique preview of work currently being written up
Preface; 1. Hereditary and monotone properties of combinatorial structures B. Bollobas; 2. Ordering classes of matrices of 0's and 1's R. A. Brualdi; 3. Cycle decompositions of complete graphs D. Bryant; 4. Excluding induced subgraphs M. Chudnovsky and P. Seymour; 5. Designs and topology M. J. Grannell and T. S. Griggs; 6. The number of points on an algebraic curve over a finite field J. W. P. Hirschfeld, G. Korchmaros and F. Torres; 7. On the efficient approximability of constraint satisfaction problems J. Hastad; 8. The combinatorics of cryptographic key establishment K. M. Martin; 9. Bandwidth of graphic matroids F. Mazoit and S. Thomasse.
'The frequent citations of the past volumes shows that these papers are very good references of contemporary research. The quality of contributors and the discussed topics ensure that the present volume will continue this tradition.' Acta Scientiarum Mathematicarum