Nonsequenceable Steiner triple systems

Abstract

A partial Steiner triple system is is $sequenceable$ if the points can be sequenced so that no proper segment can be partitioned into blocks. We show that, if $0\le a\le (n-1)/3$, then there exists a nonsequenceable PSTS$(n)$ of size $\frac{1}{3}\left(\genfrac{}{}{0ex}{}{n}{2}\right)-a$, for all $n\equiv 1(\mathrm{mod}6)$ except for $n=7$.

References in corpus (1)

• Block-avoiding sequencings of points in Steiner triple systems