Combinatorics, Geometry and Probability: A Tribute to Paul Erdös

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.

Table of Contents:
1. Some unsolved problems Paul Erdös; 2. Menger's theorem for a countable source set R. Aharoni and R. Diestel; 3. On extremal set partitions in Cartesian product spaces R. Ahlswede and N. Cai; 4. Matchings in lattice graphs and Hamming graphs M. Aigner and R. Klimmek; 5. Reconstructing a graph from its neighbourhood lists M. Aigner and E. Triesch; 6. Threshold functions for H-factors N. Alon and R. Yuster; 7. A rate for the Erdös–Turán law A. D. Barbour and S. Tavaré; 8. Deterministic graph games and a probabilistic intuition J. Beck; 9. On oriented embedding of the binary tree into the hypercube S. L. Bezrukov; 10. Potential theory on distance-regular graphs N. L. Biggs; 11. On the length of the longest increasing subsequence in a random permutation B. Bollobás and S. Janson; 12. On Richardson's model on the hypercube B. Bollobás and Y. Kohayakawa; 13. Random permutations: some group-theoretic aspects P. J. Cameron and W. M. Kantor; 14. Ramsey problems with bounded degree spread G. Chen and R. H. Schelp; 15. Hamilton cycles in random regular digraphs C. Cooper, A. Frieze and M. Molloy; 16. On triangle contact graphs H. de Fraysseix, P. Ossona de Mendez and P. Rosenstiehl; 17. A combinatorial approach to complexity theory via ordinal hierarchies W. A. Deuber and W. Thumser; 18. Lattice points of cut cones M. Deza and V. Grishukin; 19. The growth of infinite graphs: boundedness and finite spreading R. Diestel and I. Leader; 20. Amalgamated factorizations of complete graphs J. K. Dugdale and A. J. W. Hilton; 21. Ramsey size linear graphs Paul Erdös, R. J. Faudree, C. C. Rousseau and R. H. Schelp; 22. Turán–Ramsey theorems and Kp independence numbers Paul Erdös, A. Hajnal, M. Simonovits, V. T. Sós and E. Szemerédi; 23. Nearly equal distances in the plane Paul Erdös, E. Makai and J. Pach; 24. Clique partitions of chordal graphs Paul Erdös, E. T. Ordman and Y. Zalcstein; 25. On intersecting chains in Boolean algebras Péter L. Erdös, A. Seress and L. A. Szekely; 26. On the maximum number of triangles in wheel-free graphs Z. Füredi, M.X. Goemans and D. J. Kleitman; 27. Blocking sets in SQS(2v) M. Gionfriddo, S. Milici and Zs. Tuza; 28. (1,2)-factorisations of general Eulerian nearly regular graphs R. Häggkvist and A. Johansson; 29. Oriented Hamilton cycles in digraphs R. Häggkvist and A. Thomason; 30. Minimization problems for infinite n-connected graphs R. Halin; 31. On universal threshold graphs P. L. Hammer and A. K. Kelmans; 32. Image partition regularity of matrices N. Hindman and I. Leader; 33. Extremal graph problems for graphs with a color-critical vertex C. Hundack, H. J. Prömel and A. Steger; 34. A note on W1-to-W1 functions P. Komjáth; 35. Topological cliques in graphs J. Komlós and E. Szemerédi; 36. Local-global phenomena in graphs N. Linial; 37. On random generation of the symmetric group T. Luczak and L. Pyber; 38. On vertex-edge-critically n-connected graphs W. Mader; 39. On a conjecture of Erdös and Cudakov A. R. D. Mathias; 40. A random recolouring method for graphs and hypergraphs C. McDiarmid; 41. Obstructions for the disk and the cylinder embedding extension problems B. Mohar; 42. A Ramsey–type theorem in the plane J. Nesetril and P. Valtr; 43. The enumeration of self-avoiding walks and domains on a lattice H. N. V. Temperley; 44. An extension of Foster's network theorem P. Tetali; 45. Randomised approximation in the Tutte plane D. J. A. Welsh; 46. On crossing numbers, and some unsolved problems H. S. Wilf.