The Mathematics of Paul Erdos II

This is the most comprehensive survey of the mathematical life of the legendary Paul Erdos (1913-1996), one of the most versatile and prolific mathematicians of our time. For the first time, all the main areas of Erdos' research are covered in a single project. Because of overwhelming response from the mathematical community, the project now occupies over 1000 pages, arranged into two volumes. These volumes contain both high level research articles as well as key articles that survey some of the cornerstones of Erdos' work, each written by a leading world specialist in the field. A special chapter "Early Days", rare photographs, and art related to Erdos complement this striking collection. A unique contribution is the bibliography on Erdos' publications: the most comprehensive ever published. This new edition, dedicated to the 100th anniversary of Paul Erdos' birth, contains updates on many of the articles from the two volumes of the first edition, several new articles from prominent mathematicians, a new introduction, and more biographical information about Paul Erdos with an updated list of publications.

The second volume contains chapters on graph theory and combinatorics, extremal and Ramsey theory, and a section on infinity that covers Erdos' research on set theory. All of these chapters are essentially updated, particularly the extremal theory chapter that contains a survey of flag algebras, a new technique for solving extremal problems.

VOLUME II.- Part I Combinatorics and Graph Theory.- Introduction.- Reconstruction Problems for Digraphs.- Neighborly Families of Boxes and Bipartite Coverings.- On the Isolation of a Common Secret.- Properties of Graded Posets Preserved by Some Operations.- The Dimension of Random Graph Orders.- Hereditary and Monotone Properties of Graphs.- Cycles and Paths in Triangle-Free Graphs.- Problems in Graph Theory from Memphis.- Some Remarks on the Cycle Plus Triangles Problem.- Intersection Representations of the Complete Bipartite Graph.- Reflections on a Problem of Erdos and Hajnal.- The Chromatic Number of the Two-Packing of a Forest.- Part II Ramsey and Extremal Theory.- Introduction.- Ramsey Theory in the Work of Paul Erdos.- Memories on Shadows and Shadows of Memories.- A Bound of the Cardinality of Families Not Containing ?-Systems.- Flag Algebras: An Interim Report.- Arrangeability and Clique Subdivisions.- A Finite Partition Theorem with Double Exponential Bound.- Paul Erdos' Influence on Extremal Graph Theory.- Applications of the Probabilistic Method to Partially Ordered Sets.- Part III Infinity.- Introduction.- A Few Remarks on a Conjecture of Erdos on the Infinite Version of Menger's Theorem.- The Random Graph.- Paul Erdos' Set Theory.- Set Theory: Geometric and Real.- On Order-Perfect Lattices.- The PCF Theorem Revisited.- Paul Erdos: The Master of Collaboration.- List of Publications of Paul Erdos.- Postscript.

Ronald L. Graham is currently Professor of Mathematics and Irwin and Joan Jacobs Professor of Computer and Information Sciences at the University of California, San Diego, and Chief Scientist at the California Institute for Telecommunications and Information Technology.

Jaroslav Nešetril is currently Professor of Mathematics and Director of the Institute of Theoretical Computer Science at Charles University, Prague.

Steve Butler is currently Assistant Professor of Mathematics at Iowa State University.