This is the most comprehensive survey of the mathematical life of the legendary Paul Erdős (1913-1996), one of the most versatile and prolific mathematicians of our time. For the first time, all the main areas of Erdős' 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 Erdős' work, each written by a leading world specialist in the field. A special chapter "Early Days", rare photographs, and art related to Erdős complement this striking collection. A unique contribution is the bibliography on Erdős' publications: the most comprehensive ever published. This new edition, dedicated to the 100th anniversary of Paul Erdős' 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 Erdős 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 Erdős' 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.
Author(s): Martin Aigner, Eberhad Triesch (auth.), Ronald L. Graham, Jaroslav Nešetřil, Steve Butler (eds.)
Edition: 2
Publisher: Springer-Verlag New York
Year: 2013
Language: English
Pages: 607
Tags: Mathematics, general; Combinatorics; Graph Theory; Mathematical Logic and Foundations
Front Matter....Pages i-xix
Front Matter....Pages 1-4
Reconstruction Problems for Digraphs....Pages 5-13
Neighborly Families of Boxes and Bipartite Coverings....Pages 15-20
On the Isolation of a Common Secret....Pages 21-38
Properties of Graded Posets Preserved by Some Operations....Pages 39-46
The Dimension of Random Graph Orders....Pages 47-68
Hereditary and Monotone Properties of Graphs....Pages 69-80
Cycles and Paths in Triangle-Free Graphs....Pages 81-93
Problems in Graph Theory from Memphis....Pages 95-118
Some Remarks on the Cycle Plus Triangles Problem....Pages 119-125
Intersection Representations of the Complete Bipartite Graph....Pages 127-134
Reflections on a Problem of Erdős and Hajnal....Pages 135-141
The Chromatic Number of the Two-Packing of a Forest....Pages 143-166
Front Matter....Pages 167-170
Ramsey Theory in the Work of Paul Erdős....Pages 171-193
Memories on Shadows and Shadows of Memories....Pages 195-198
A Bound of the Cardinality of Families Not Containing $$\Delta $$ -Systems....Pages 199-206
Flag Algebras: An Interim Report....Pages 207-232
Arrangeability and Clique Subdivisions....Pages 233-236
A Finite Partition Theorem with Double Exponential Bound....Pages 237-244
Paul Erdős’ Influence on Extremal Graph Theory....Pages 245-311
Applications of the Probabilistic Method to Partially Ordered Sets....Pages 313-329
Front Matter....Pages 331-333
A Few Remarks on a Conjecture of Erdős on the Infinite Version of Menger’s Theorem....Pages 335-352
The Random Graph....Pages 353-378
Paul Erdős’ Set Theory....Pages 379-418
Set Theory: Geometric and Real....Pages 419-425
On Order-Perfect Lattices....Pages 427-439
The PCF Theorem Revisited....Pages 441-488
Paul Erdős: The Master of Collaboration....Pages 489-496
Back Matter....Pages 497-607
