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

Frontmatter
pp i-iv
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Contents
pp v-viii
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Preface
pp ix-x
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Farewell to Paul Erdős
pp xi-xii
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Toast to Paul Erdős
pp xiii-xvi
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List of Contributors
pp xvii-xxii
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Paul Erdős: Some Unsolved Problems
pp 1-10
- By Paul Erdős
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Menger's Theorem for a Countable Source Set
pp 11-22
- By R. Aharoni, Department of Mathematics, Technion, Haifa 32000, Israel, R. Diestel, Mathematical Institute, Oxford University, Oxford OX1 3LB, England
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On Extremal Set Partitions in Cartesian Product Spaces
pp 23-32
- By R. Ahlswede, Universität Bielefeld, Fakultät für Mathematik, Postfach 100131, 33501 Bielefeld, Germany, N. Cai, Universität Bielefeld, Fakultät für Mathematik, Postfach 100131, 33501 Bielefeld, Germany
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Matchings in Lattice Graphs and Hamming Graphs
pp 33-50
- By M. Aigner, II. Mathematisches Institut, Freie Universität Berlin, Arnimallee 3, D-14195 Berlin, R. Klimmek, II. Mathematisches Institut, Freie Universität Berlin, Arnimallee 3, D-14195 Berlin
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Reconstructing a Graph from its Neighborhood Lists
pp 51-62
- By M. Aigner, Freie Universität Berlin, Fachbereich Mathematik, WE 2, Arnimallee 3, 1000 Berlin 33, Germany, E. Triesch, Forschungsinsitut für Diskrete Mathematik, Nassestraße 2, 5300 Bonn 1, Germany
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Threshold Functions for H-factors
pp 63-70
- By N. Alon, Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel, R. Yuster, Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel
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A Rate for the Erdős–Turán Law
pp 71-80
- By A.D. Barbour, Institut für Angewandte Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057, Zürich, Switzerland, S. Tavaré, Department of Mathematics, University of Southern California, Los Angeles, CA 90089-1113
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Deterministic Graph Games and a Probabilistic Intuition
pp 81-94
- By J. Beck, Department of Mathematics, Rutgers University, Busch Campus, Hill Center, New Brunswick, New Jersey 08903 U.S.A.
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On Oriented Embedding of the Binary Tree into the Hypercube
pp 95-106
- By S.L. Bezrukov, Fachbereich Mathematik, Freie Universität Berlin, Arnimallee 2–6, D-14195 Berlin
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Potential Theory on Distance-Regular Graphs
pp 107-120
- By N.L. Biggs, London School of Economics, Houghton St., London WC2A 2AE
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On the Length of the Longest Increasing Subsequence in a Random Permutation
pp 121-128
- By B. Bollobás, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, England, S. Janson, Department of Mathematics, Uppsala University, PO Box 480, S-751 06 Uppsala, Sweden
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On Richardson's Model on the Hypercube
pp 129-138
- By B. Bollobás, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, England, Y. Kohayakawa, Instituto de Matemática e Estatística, Universidade de Sāo Paulo, Caixa Postal 20570, 01452–990 São Paulo, SP, Brazil
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Random Permutations: Some Group-Theoretic Aspects
pp 139-144
- By P.J. Cameron, School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London El 4NS, U.K., W.M. Kantor, Department of Mathematics, University of Oregon, Eugene, OR 97403, U.S.A.
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Ramsey Problems with Bounded Degree Spread
pp 145-152
- By G. Chen, North Dakota State University, Fargo, ND 58105, R.H. Schelp, Memphis State University, Memphis, TN 38152
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Hamilton Cycles in Random Regular Digraphs
pp 153-164
- By C. Cooper, School of Mathematical Sciences, University of North London, London, U.K., A. Frieze, Department of Mathematics, Carnegie-Mellon University, Pittsburgh PA15213, U.S.A., M. Molloy, Department of Mathematics, Carnegie-Mellon University, Pittsburgh PA15213, U.S.A.
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On Triangle Contact Graphs
pp 165-178
- By H. de Fraysseix, CNRS, EHESS, 54 Boulevard Raspail, 75006, Paris, France, P. Ossona de Mendez, CNRS, EHESS, 54 Boulevard Raspail, 75006, Paris, France, P. Rosenstiehl, CNRS, EHESS, 54 Boulevard Raspail, 75006, Paris, France
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A Combinatorial Approach to Complexity Theory via Ordinal Hierarchies
pp 179-192
- By W.A. Deuber, University of Bielefeld, Faukultät Mathematik, Postfach 10 01 31 33501 Bielefeld 1, Germany, W. Thumser, University of Bielefeld, Faukultät Mathematik, Postfach 10 01 31 33501 Bielefeld 1, Germany
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Lattice Points of Cut Cones
pp 193-216
- By M. Deza, CNRS-LIENS, Ecole Normale Supérieure, Paris, V. Grishukhin, Central Economic and Mathematical Institute of Russian Academy of Sciences (CEMI RAN), Moscow
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The Growth of Infinite Graphs: Boundedness and Finite Spreading
pp 217-222
- By R. Diestel, Faculty of Mathematics (SFB 343), Bielefeld University, D-4800 Bielefeld, Germany, I. Leader, Department of Pure Mathematics, University of Cambridge, 16 Mill Lane, Cambridge, CB2 1SB England
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Amalgamated Factorizations of Complete Graphs
pp 223-240
- By J.K. Dugdale, Department of Mathematics, West Virginia University, PO Box 6310, Morgantown WV 26506-6310, U.S.A., A.J.W. Hilton, Department of Mathematics, University of Reading, Whiteknights, PO Box 220, Reading RG6 2AX. U.K.
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Ramsey Size Linear Graphs
pp 241-252
- By Paul Erdős, Mathematical Institute, Hungarian Academy of Sciences, Budapest V, Hungary, R.J. Faudree, Department of Mathematical Science, Memphis State University, Tenn. 38152 USA, C.C. Rousseau, Department of Mathematical Science, Memphis State University, Tenn. 38152 USA, R.H. Schelp, Department of Mathematical Science, Memphis State University, Tenn. 38152 USA
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Turán–Ramsey Theorems and Kp-Independence Numbers
pp 253-282
- By Paul Erdős, Mathematical Institute of the Hungarian Academy of Sciences, Budapest, A. Hajnal, Mathematical Institute of the Hungarian Academy of Sciences, Budapest, M. Simonovits, Mathematical Institute of the Hungarian Academy of Sciences, Budapest, V.T. Sós, Mathematical Institute of the Hungarian Academy of Sciences, Budapest, E. Szemerédi, Mathematical Institute of the Hungarian Academy of Sciences, Budapest
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Nearly Equal Distances in the Plane
pp 283-290
- By Paul Erdős, Mathematical Institute of the Hungarian Academy of Sciences, E. Makai, Department of Computer Science, City College, New York, and Mathematical Institute of the Hungarian Academy of Sciences, J. Pach, Department of Computer Science, City College, New York, and Mathematical Institute of the Hungarian Academy of Sciences
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Clique Partitions of Chordal Graphs
pp 291-298
- By Paul Erdős, Mathematical Institute, Hungarian Academy of Sciences, E.T. Ordman, Memphis State University, Memphis, TN 38152 U.S.A, Y. Zalcstein, Division of Computer and Computation Research, National Science Foundation, Washington, D. C. 20550, U. S. A
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Combinatorics, Geometry and Probability

A Tribute to Paul Erdös

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