ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

13. Combinatorics

1991 MS Classification: 05C Thomason, Andrew, University of Cambridge Hereditary hypergraph properties A hypergraph property P is hereditary if it is preserved under the taking of induced subgraphs. An inequality concerning projections of Euclidean bodies implies a monotonicity condition for the probability that a randomly generated hypergraph has P; the size of P is similarly monotonic. The probability can be approximated by that of regular properties, so determining the P-chromatic number of almost all graphs. The material is joint with Béla Bollobás and is related to the subject of his invited lecture. Reference: B. Bollobás and A. Thomason, Projections of bodies and hereditary properties of hypergraphs, J. London Math. Soc. 27 (1995) 417–424.