Ebook: The Mathematics of Paul Erdös II

This is the most comprehensive survey of the mathematical life of the legendary Paul Erd?s, one of the most versatile and prolific mathematicians of our time. For the first time, all the main areas of Erd?s' research are covered in a single project. Because of overwhelming response from the mathematical community, the project now occupies over 900 pages, arranged into two volumes. These volumes contain both high level research articles as well as "key" articles which survey some of the cornerstones of Erd?s' work, each written by a leading world specialist in the field. A special chapter "Early Days", rare photographs, and art related to Erd?s complement this striking collection. A unique contribution is the bibliography on Erd?s' publications: the most comprehensive ever published.

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This is the most comprehensive survey of the mathematical life of the legendary Paul Erd?s, one of the most versatile and prolific mathematicians of our time. For the first time, all the main areas of Erd?s' research are covered in a single project. Because of overwhelming response from the mathematical community, the project now occupies over 900 pages, arranged into two volumes. These volumes contain both high level research articles as well as "key" articles which survey some of the cornerstones of Erd?s' work, each written by a leading world specialist in the field. A special chapter "Early Days", rare photographs, and art related to Erd?s complement this striking collection. A unique contribution is the bibliography on Erd?s' publications: the most comprehensive ever published.
Content:
Front Matter....Pages I-XVI
Front Matter....Pages 1-1
Introduction....Pages 3-6
Problems in Graph Theory from Memphis....Pages 7-26
Neighborly Families of Boxes and Bipartite Coverings....Pages 27-31
Cycles and Paths in Triangle-Free Graphs....Pages 32-42
Reconstruction Problems for Digraphs....Pages 43-50
The Dimension of Random Graph Orders....Pages 51-69
Hereditary and Monotone Properties of Graphs....Pages 70-78
Properties of Graded Posets Preserved by Some Operations....Pages 79-85
Intersection Representations of the Complete Bipartite Graph....Pages 86-92
Reflections on a Problem of Erd?s and Hajnal....Pages 93-98
The Chromatic Number of the Two-packing of a Forest....Pages 99-120
On the Isolation of a Common Secret....Pages 121-135
Some Remarks on the Cycle Plus Triangles Problem....Pages 136-142
Front Matter....Pages 143-143
Introduction....Pages 145-147
Paul Erd?s’ Influence on Extremal Graph Theory....Pages 148-192
Ramsey Theory in the Work of Paul Erd?s....Pages 193-209
Memories on Shadows and Shadows of Memories....Pages 210-213
Applications of the Probabilistic Method to Partially Ordered Sets....Pages 214-228
A Bound of the Cardinality of Families not Containing ?-Systems....Pages 229-235
Arrangeability and Clique Subdivisions....Pages 236-239
Front Matter....Pages 143-143
A Finite Partition Theorem with Double Exponential Bound....Pages 240-246
Front Matter....Pages 247-247
Introduction....Pages 249-250
Extension of Functional Equations....Pages 251-263
Remarks on Penrose Tilings....Pages 264-283
Distances in Convex Polygons....Pages 284-293
The Number of Homothetic Subsets....Pages 294-302
On Lipschitz Mappings onto a Square....Pages 303-309
A Remark on Transversal Numbers....Pages 310-317
In Praise of the Gram Matrix....Pages 318-323
On Mutually Avoiding Sets....Pages 324-328
Front Matter....Pages 329-329
Introduction....Pages 331-332
The Random Graph....Pages 333-351
Paul Erd?s’ Set Theory....Pages 352-393
A Few Remarks on a Conjecture of Erd?s on the Infinite Version of Menger’s Theorem....Pages 394-408
On Order-Perfect Lattices....Pages 409-419
The PCF Theorem Revisited....Pages 420-459
Set Theory: Geometric and Real....Pages 460-466
Back Matter....Pages 467-577

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This is the most comprehensive survey of the mathematical life of the legendary Paul Erd?s, one of the most versatile and prolific mathematicians of our time. For the first time, all the main areas of Erd?s' research are covered in a single project. Because of overwhelming response from the mathematical community, the project now occupies over 900 pages, arranged into two volumes. These volumes contain both high level research articles as well as "key" articles which survey some of the cornerstones of Erd?s' work, each written by a leading world specialist in the field. A special chapter "Early Days", rare photographs, and art related to Erd?s complement this striking collection. A unique contribution is the bibliography on Erd?s' publications: the most comprehensive ever published.
Content:
Front Matter....Pages I-XVI
Front Matter....Pages 1-1
Introduction....Pages 3-6
Problems in Graph Theory from Memphis....Pages 7-26
Neighborly Families of Boxes and Bipartite Coverings....Pages 27-31
Cycles and Paths in Triangle-Free Graphs....Pages 32-42
Reconstruction Problems for Digraphs....Pages 43-50
The Dimension of Random Graph Orders....Pages 51-69
Hereditary and Monotone Properties of Graphs....Pages 70-78
Properties of Graded Posets Preserved by Some Operations....Pages 79-85
Intersection Representations of the Complete Bipartite Graph....Pages 86-92
Reflections on a Problem of Erd?s and Hajnal....Pages 93-98
The Chromatic Number of the Two-packing of a Forest....Pages 99-120
On the Isolation of a Common Secret....Pages 121-135
Some Remarks on the Cycle Plus Triangles Problem....Pages 136-142
Front Matter....Pages 143-143
Introduction....Pages 145-147
Paul Erd?s’ Influence on Extremal Graph Theory....Pages 148-192
Ramsey Theory in the Work of Paul Erd?s....Pages 193-209
Memories on Shadows and Shadows of Memories....Pages 210-213
Applications of the Probabilistic Method to Partially Ordered Sets....Pages 214-228
A Bound of the Cardinality of Families not Containing ?-Systems....Pages 229-235
Arrangeability and Clique Subdivisions....Pages 236-239
Front Matter....Pages 143-143
A Finite Partition Theorem with Double Exponential Bound....Pages 240-246
Front Matter....Pages 247-247
Introduction....Pages 249-250
Extension of Functional Equations....Pages 251-263
Remarks on Penrose Tilings....Pages 264-283
Distances in Convex Polygons....Pages 284-293
The Number of Homothetic Subsets....Pages 294-302
On Lipschitz Mappings onto a Square....Pages 303-309
A Remark on Transversal Numbers....Pages 310-317
In Praise of the Gram Matrix....Pages 318-323
On Mutually Avoiding Sets....Pages 324-328
Front Matter....Pages 329-329
Introduction....Pages 331-332
The Random Graph....Pages 333-351
Paul Erd?s’ Set Theory....Pages 352-393
A Few Remarks on a Conjecture of Erd?s on the Infinite Version of Menger’s Theorem....Pages 394-408
On Order-Perfect Lattices....Pages 409-419
The PCF Theorem Revisited....Pages 420-459
Set Theory: Geometric and Real....Pages 460-466
Back Matter....Pages 467-577
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