Graham, Ronald L., Nešetřil, Jaroslav, Butler, Steve (Eds.)
2nd ed. 2013, XIX, 607 p. 66 illus., 2 illus. in color.
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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.
Content Level » Research
Keywords » Erdős existence argument - Erdős–Turán - Paul Erdős - Ramsey theory - additive representation functions - extremal theory - incidence problems - probabilistic method - sum-product phenomena
Related subjects » Mathematics
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 Erdős 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 Erdős.- Memories on Shadows and Shadows of Memories.- A Bound of the Cardinality of Families Not Containing Δ-Systems.- Flag Algebras: An Interim Report.- Arrangeability and Clique Subdivisions.- A Finite Partition Theorem with Double Exponential Bound.- Paul Erdős' 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 Erdős on the Infinite Version of Menger's Theorem.- The Random Graph.- Paul Erdős' Set Theory.- Set Theory: Geometric and Real.- On Order-Perfect Lattices.- The PCF Theorem Revisited.- Paul Erdős: The Master of Collaboration.- List of Publications of Paul Erdős.- Postscript.
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