The study of random graphs was begun in the 1960s and now has a comprehensive literature. This excellent book by one of the top researchers in the field now joins the study of random graphs (and other random discrete objects) with mathematical logic. The methodologies involve probability, discrete structures and logic, with an emphasis on discrete structures.

The study of random graphs was begun in the 1960s and now has a comprehensive literature. This excellent book by one of the top researchers in the field now joins the study of random graphs (and other random discrete objects) with mathematical logic. The methodologies involve probability, discrete structures and logic, with an emphasis on discrete structures.

From social networks such as Facebook, the World Wide Web and the Internet, to the complex interactions between proteins in the cells of our bodies, we constantly face the challenge of understanding the structure and development of networks. The theory of random graphs provides a framework for this understanding, and in this book the authors give a gentle introduction to the basic tools for understanding and applying the theory. Part I includes sufficient material, including exercises, for a one semester course at the advanced undergraduate or beginning graduate level. The reader is then well prepared for the more advanced topics in Parts II and III. A final part provides a quick introduction to the background material needed. All those interested in discrete mathematics, computer science or applied probability and their applications will find this an ideal introduction to the subject.

In the ten years since the publication of the best-selling first edition, more than 1,000 graph theory papers have been published each year. Reflecting these advances, Handbook of Graph Theory, Second Edition provides comprehensive coverage of the main topics in pure and applied graph theory. This second edition-over 400 pages longer than its prede

Model theory is one of the central branches of mathematical logic. The field has evolved rapidly in the last few decades. This book is an introduction to current trends in model theory, and contains a collection of articles authored by top researchers in the field. It is intended as a reference for students as well as senior researchers.

This volume contains the papers presented at the 30th Symposium on Mathematical Foundations of Computer Science (MFCS 2005) held in Gdansk, Poland from August 29th to September 2nd, 2005.

TCC 2005, the 2nd Annual Theory of Cryptography Conference, was held in Cambridge,Massachusetts,onFebruary10–12,2005.Theconferencereceived84 submissions,ofwhichtheprogramcommitteeselected32forpresentation.These proceedings contain the revised versions of the submissions that were presented at the conference. These revisions have not been checked for correctness, and the authors bear full responsibility for the contents of their papers. The conference program also included a panel discussion on the future of theoretical cryptography and its relationship to the real world (whatever that is). It also included the traditional “rump session,” featuring short, informal talks on late-breaking research news. Much as hatters of old faced mercury-induced neurological damage as an occupational hazard, computer scientists will on rare occasion be a?icted with egocentrism, probably due to prolonged CRT exposure. Thus, you must view withpityandnotcontemptmyunalloyedelationathavingmynameonthefront cover of this LNCS volume, and my deep-seated conviction that I fully deserve the fame and riches that will surely come of it. However, having in recent years switched over to an LCD monitor, I would like to acknowledge some of the many who contributed to this conference. First thanks are due to the many researchers from all over the world who submitted their work to this conference. Lacking shrimp and chocolate-covered strawberries, TCC has to work hard to be a good conference. As a community, I think we have.