NSF/CBMS Regional Research Conference
in Mathematical Sciences on
Geometric Graph Theory

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Principal Lecturer
JŠnos Pach

Subject
Geometric Graph Theory

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May 28 - June 1, 2002
Gateway Center

University of North Texas, Denton

Principal Lecturer 


János Pach is Professor of Computer Science at City College (CUNY), Research Professor at the Courant Institute (NYU) and at the Rényi Institute (Hungarian Academy of Sciences). He has published the monograph Combinatorial Geometry (with P. K. Agarwal, Wiley, 1995) and about 150 research papers. He serves on the editorial boards of five technical journals and is a recipient of the Lester Ford Award (Mathematical Assocation of America, 1990), the Rényi Award (1993) and the Academy Award (Hungarian Academy of Sciences, 1998).

Among other results, Professor Pach

  • settled Ulam's problem by showing that there exist no universal countable graphs (1981);
  • together with Bárány and Füredi verified L. Fejes Tóth's Six Circle Conjecture, stating that in any 6-neighbored circle packing in the plane either all circles are of the same size, or there are arbitrarily small circles (1984);
  • together with de Fraysseix and Pollack discovered the first efficient algorithm for drawing a planar graph using straight line edges on a linear sized grid, and thus solved a famous open problem of Rosenstiehl and Tarjan (1990);
  • together with Törocsik proved the conjecture of Erdos, Hanani, and Perles, stating that for every k the number of edges of a geometric graph of n vertices having no k pairwise disjoint edges is O(n) (1994);
  • proved that there is a constant \lceil Cd \rceil such that any n-element sets P1, . . . , Pd+1 in general position in d-space have Cd n-element subsets Q1, . . . , Qd+1 such that all simplices induced by picking one point from each Qi have an interior point in common (1998);
  • together with G. Tóth solved a 40 years old problem of Benzer, Sinden, Graham, and Kratochvil, showing that the recognition of "string graphs" (i.e., intersection graphs of plane Jordan curves) is decidable (2000).

Professor Pach has given many lectures on Geometric Graph Theory, including a one-hour plenary address at the Annual Meeting of the American Mathematical Society (Atlanta, 1996) and the Sixth Annual Charles H. Franke Memorial Lecture (Seton Hall, 2000). He was a principal speaker at the British Combinatorial Conference (Canterbury, 1999). The text of this latter lecture, published in the London Mathematical Society Lecture Note Series, is the most comprehensive survey of Geometric Graph Theory.