ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

13. Combinatorics

1991 MS Classification: 05B35 McNulty, Jennifer, The University of Montana, USA, Wu, Haidong, Southern University, USA Connected Hyperplanes in Binary Matroids As many simple cosimple connected matroids have no connected hyperplanes, it is a somewhat surprising result (due to Seymour) that simple cosimple connected binary matroids have at least one connected hyperplane. We strengthen this result to prove such matroids have at least four connected hyperplanes. In addition, we show the bound is best possible. This extends related graph theory results of Thomassen and Toft and of Kaugars.