The Mathematics of Paul Erdös II

1. Front Matter

   Pages I-XVI

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2. Combinatorics and Graph theory

   1. Front Matter

      Pages 1-1

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   2. Introduction

      • Ronald L. Graham, Jaroslav Nešetřil

      Pages 3-6

   3. Problems in Graph Theory from Memphis

      • R. J. Faudree, C. C. Rousseau, R. H. Schelp

      Pages 7-26

   4. Neighborly Families of Boxes and Bipartite Coverings

      • Noga Alon

      Pages 27-31

   5. Cycles and Paths in Triangle-Free Graphs

      • Stephan Brandt

      Pages 32-42

   6. Reconstruction Problems for Digraphs

      • M. Aigner, E. Triesch

      Pages 43-50

   7. The Dimension of Random Graph Orders

      • Béla Bollobás, Graham Brightwell

      Pages 51-69

   8. Hereditary and Monotone Properties of Graphs

      • Béla Bollobás, Andrew Thomason

      Pages 70-78

   9. Properties of Graded Posets Preserved by Some Operations

      • Sergej Bezrukov, Konrad Engel

      Pages 79-85

   10. Intersection Representations of the Complete Bipartite Graph

       • Zoltän Füredi

       Pages 86-92

   11. Reflections on a Problem of Erdős and Hajnal

       • András Gyárfás

       Pages 93-98

   12. The Chromatic Number of the Two-packing of a Forest

       • Hong Wang, Norbert Sauer

       Pages 99-120

   13. On the Isolation of a Common Secret

       • Don Beaver, Stuart Haber, Peter Winkler

       Pages 121-135

   14. Some Remarks on the Cycle Plus Triangles Problem

       • H. Fleischner, M. Stiebitz

       Pages 136-142

3. Ramsey and Extremal Theory

   1. Front Matter

      Pages 143-143

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   2. Introduction

      • Ronald L. Graham, Jaroslav Nešetřil

      Pages 145-147

   3. Paul Erdős’ Influence on Extremal Graph Theory

      • Miklós Simonovits

      Pages 148-192

   4. Ramsey Theory in the Work of Paul Erdős

      • R. L. Graham, J. Nešetřil

      Pages 193-209

   5. Memories on Shadows and Shadows of Memories

      • G. O. H. Katona

      Pages 210-213

In 1992, when Paul Erdos was awarded a Doctor Honoris Causa by Charles University in Prague, a small conference was held, bringing together a distin­ guished group of researchers with interests spanning a variety of fields related to Erdos' own work. At that gathering, the idea occurred to several of us that it might be quite appropriate at this point in Erdos' career to solicit a col­ lection of articles illustrating various aspects of Erdos' mathematical life and work. The response to our solicitation was immediate and overwhelming, and these volumes are the result. Regarding the organization, we found it convenient to arrange the papers into six chapters, each mirroring Erdos' holistic approach to mathematics. Our goal was not merely a (random) collection of papers but rather a thor­ oughly edited volume composed in large part by articles explicitly solicited to illustrate interesting aspects of Erdos and his life and work. Each chap­ ter includes an introduction which often presents a sample of related Erdos' problems "in his own words". All these (sometimes lengthy) introductions were written jointly by editors. We wish to thank the nearly 70 contributors for their outstanding efforts (and their patience). In particular, we are grateful to Bela Bollobas for his extensive documentation of Paul Erdos' early years and mathematical high points (in the first part of this volume); our other authors are acknowledged in their respective chapters. We also want to thank A. Bondy, G. Hahn, I.

• Combinatorics
• Lattice
• Partition
• Ramsey theory
• graph theory
• mapping
• number theory
• set theory

• AT&T Bell Laboratories, Murray Hill, USA

  Ronald L. Graham

• Department of Applied Mathematics, Charles University, Praha, Czech Republic

  Jaroslav Nešetřil

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