Combinatorics, Geometry and Probability: A Tribute to Paul Erdös

doi:10.1017/CBO9780511662034

Paul Erdös was one of the greatest mathematicians of this century, known the world over for his brilliant ideas and stimulating questions. On the date of his 80th birthday a conference was held in his honour at Trinity College, Cambridge. Many leading combinatorialists attended. Their subsequent contributions are collected here. The areas represented range from set theory and geometry, through graph theory, group theory and combinatorial probability, to randomised algorithms and statistical physics. Erdös himself was able to give a survey of recent progress made on his favourite problems. Consequently this volume, consisting of in-depth studies at the frontier of research, provides a valuable panorama across the breadth of combinatorics as it is today.

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Contents

On Intersecting Chains in Boolean Algebras
pp 299-304
- By Péter L. Erdős, Centrum voor Wiskunde en Informatica, P.O. Box 4079, 1009 AB Amsterdam, The Netherlands, Á. Seress, The Ohio State University, Columbus, OH 43210, L.A. Székely, University of New Mexico, Albuquerque, NM 87131
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On the Maximum Number of Triangles in Wheel-Free Graphs
pp 305-318
- By Z. Füredi, Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, M.X. Goemans, Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, D.J. Kleitman, Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139
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Blocking Sets in SQS(2v)
pp 319-328
- By M. Gionfriddo, Dipartimento di Matematica, Città Universitaria, Viale A, Doria 6, 95125 Catania, Italy, S. Milici, Dipartimento di Matematica, Città Universitaria, Viale A, Doria 6, 95125 Catania, Italy, Z. Tuza, Computer and Automation Institute, Hungarian Academy of Sciences H-1111 Budapest, Kende u. 13–17, Hungary
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(1,2)-Factorizations of General Eulerian Nearly Regular Graphs
pp 329-338
- By R. Häggkvist, Department of Mathematics, University of Umeá, S-901 87 Umeá, Sweden, A. Johansson, Department of Mathematics, University of Umeá, S-901 87 Umeá, Sweden
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Oriented Hamilton Cycles in Oriented Graphs
pp 339-354
- By R. Häggkvist, Department of Mathematics, University of Umeå, S-901 87 Umeå, Sweden, A. Thomason, DPMMS, 16 Mill Lane, Cambridge CB2 1SB, England
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Minimization Problems for Infinite n-Connected Graphs
pp 355-374
- By R. Halin, Mathematisches Seminar der Universität Hamburg, Bundesstraße 55, D-20146, Hamburg, Germany
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On Universal Threshold Graphs
pp 375-392
- By P.L. Hammer, RUTCOR, Rutgers University New Brunswick, New Jersey 08903, A.K. Kelmans, RUTCOR, Rutgers University New Brunswick, New Jersey 08903
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Image Partition Regularity of Matrices
pp 393-420
- By N. Hindman, Department of Mathematics, Howard University, Washington, D.C. 20059, U.S.A, I. Leader, Department of Pure Mathematics and Mathematical Statistics, Cambridge University, England
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Extremal Graph Problems for Graphs with a Color-Critical Vertex
pp 421-434
- By C. Hundack, Institut für Diskrete Mathematik, Universität Bonn, Nassestr. 2, 53113 Bonn, Germany, H.J. Prömel, Institut für Diskrete Mathematik, Universität Bonn, Nassestr. 2, 53113 Bonn, Germany, A. Steger, Institut für Diskrete Mathematik, Universität Bonn, Nassestr. 2, 53113 Bonn, Germany
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A Note on ω1 → ω1 Functions
pp 435-438
- By P. Komjáth, Dept. Comp. Sci. Eötvös University, Budapest, Múzeum krt 6–8, 1088, Hungary
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Topological Cliques in Graphs
pp 439-448
- By J. Komlós, Rutgers University and Hungarian Academy of Sciences, E. Szemerédi, Rutgers University and Hungarian Academy of Sciences
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Local-Global Phenomena in Graphs
pp 449-462
- By N. Linial, Institute of Computer Science, Hebrew University, Jerusalem, Israel
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On Random Generation of the Symmetric Group
pp 463-470
- By T. Luczak, Mathematical Institute of the Polish Academy of Sciences, Poznań, Poland, L. Pyber, Mathematical Institute of the Hungarian Academy of Sciences, Budapest, Hungary
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On Vertex-Edge-Critically n-Connected Graphs
pp 471-486
- By W. Mader, Institut für Mathematik, Universität Hanover, 30167 Hanover, Weifengarten 1, Germany
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On a Conjecture of Erdős and Čudakov
pp 487-488
- By A.R.D. Mathias, Peterhouse, Cambridge
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A Random Recolouring Method for Graphs and Hypergraphs
pp 489-492
- By C. McDiarmid, Department of Statistics, University of Oxford
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Obstructions for the Disk and the Cylinder Embedding Extension Problems
pp 493-524
- By B. Mohar, Department of Mathematics, University of Ljubljana, Jadranska 19, 61111 Ljubljana, Slovenia
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A Ramsey-Type Theorem in the Plane
pp 525-534
- By J. Nešetřil, Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00 Praha 1, Czech Republic, P. Valtr, Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00 Praha 1, Czech Republic; Graduiertenkolleg ‘Algorithmische Diskrete Mathematik’, Fachbereich Mathematik, Freie Universität Berlin, Takustrasse 9, 14194 Berlin, Germany
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The Enumeration of Self-Avoiding Walks and Domains on a Lattice
pp 535-540
- By H.N.V. Temperley, Emeritus Professor of Applied Mathematics, Swansea, Wales, U.K. Thorney House, Thorney, Langport, Somerset, U.K
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An Extension of Foster's Network Theorem
pp 541-548
- By P. Tetali, AT & T Bell Labs, Murray Hill, NJ 07974
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Randomised Approximation in the Tutte Plane
pp 549-556
- By D.J.A. Welsh, Mathematical Institute and Merton College, University of Oxford
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On Crossing Numbers, and some Unsolved Problems
pp 557-562
- By H.S. Wilf, University of Pennsylvania, Philadelphia, PA 19104-6395
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Combinatorics, Geometry and Probability

A Tribute to Paul Erdös

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Contents

On Intersecting Chains in Boolean Algebras
pp 299-304

On the Maximum Number of Triangles in Wheel-Free Graphs
pp 305-318

Blocking Sets in SQS(2v)
pp 319-328

(1,2)-Factorizations of General Eulerian Nearly Regular Graphs
pp 329-338

Oriented Hamilton Cycles in Oriented Graphs
pp 339-354

Minimization Problems for Infinite n-Connected Graphs
pp 355-374

On Universal Threshold Graphs
pp 375-392

Image Partition Regularity of Matrices
pp 393-420

Extremal Graph Problems for Graphs with a Color-Critical Vertex
pp 421-434

A Note on ω1 → ω1 Functions
pp 435-438

Topological Cliques in Graphs
pp 439-448

Local-Global Phenomena in Graphs
pp 449-462

On Random Generation of the Symmetric Group
pp 463-470

On Vertex-Edge-Critically n-Connected Graphs
pp 471-486

On a Conjecture of Erdős and Čudakov
pp 487-488

A Random Recolouring Method for Graphs and Hypergraphs
pp 489-492

Obstructions for the Disk and the Cylinder Embedding Extension Problems
pp 493-524

A Ramsey-Type Theorem in the Plane
pp 525-534

The Enumeration of Self-Avoiding Walks and Domains on a Lattice
pp 535-540

An Extension of Foster's Network Theorem
pp 541-548

Randomised Approximation in the Tutte Plane
pp 549-556

On Crossing Numbers, and some Unsolved Problems
pp 557-562

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Combinatorics, Geometry and Probability

A Tribute to Paul Erdös

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