The largest Erdős–Ko–Rado sets in 2 - (v, k, 1) designs
Abstract
An Erdős–Ko–Rado set in a block design is a set of pairwise intersecting blocks. In this article we study Erdős–Ko–Rado sets in 2-(v,k,1) designs, Steiner systems. The Steiner triple systems and other special classes are treated separately. For k≥4, we prove that the largest Erdős–Ko–Rado sets cannot be larger than a point-pencil if (Formula presented) and that the largest Erdős–Ko–Rado sets are point-pencils if also r≠k2-k+1 and (r,k)≠(8, 4). For unitals we also determine an upper bound on the size of the second-largest maximal Erdős–Ko–Rado sets.
Publication Title
Designs, Codes, and Cryptography
Recommended Citation
De Boeck, M. (2015). The largest Erdős–Ko–Rado sets in 2 - (v, k, 1) designs. Designs, Codes, and Cryptography, 75 (3), 465-481. https://doi.org/10.1007/s10623-014-9929-5
