The Strange Logic of Random Graphs [Hardcover]

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.

I. Beginnings.- 0. Two Starting Examples.- 1. Preliminaries.- 2. The Ehrenfeucht Game.- II. Random Graphs.- 3. Very Sparse Graphs.- 4. The Combinatorics of Rooted Graphs.- 5. The Janson Inequality.- 6. The Main Theorem.- 7. Countable Models.- 8. Near Rational Powers of n.- III. Extras.- 9. A Dynamic View.- 10. Strings.- 11. Stronger Logics.- 12. Three Final Examples.

From the reviews of the first edition:

The author & is a leading expert in random graph theory, and reputed for his expository style. His recent book is again a well-written and exciting text, which I warmly recommend to researchers and graduate students interested in the subject. & The book has a clear and vivid style, and the material is essentially self-contained, so it is very well-suited for self-study. (P?ter Mester, Acta Scientiarum Mathematicarum, Vol. 69, 2003)

This beautifully written book deals with the fascinating world of random graphs, using a nice blend of techniques coming from combinatorics, probability and mathematical logic, while keeping the treatment self-contained. (Alessandro Berarducci, Mathematical Reviews, Issue 2003 d)

Random Graphs are a research field of major importance in discrete mathematics. This is an excellent book by one of the top researchers in this fieldDE