A class of Steiner systems S(2,4,v) with arcs of extremal size

Rok, strany: 2007, 153 - 162

An arc in a Steiner system $S=$S($2,4,v$) of order $v$ is a point set that contains at most two elements from each block. The largest size of an arc in $S$ is denoted by $α₂(S)$. The upper bound $α₂leqslant((v+2) / (3))$ is always valid; an arc with $((v+2) / (3))$ points is called a maximum arc. We present a recursive construction with the following properties:

1. From two systems $S'=$ S($2,4,v'$) and $S''=$ S($2,4,v''$) of respective orders $v'$ and $v''$, an $S=$ S($2,4,v$) of order $v=((1) / (3))(v'-1)(v''-1)+1$ is obtained.
2. $α₂(S)-1geqslant(α₂(S')-1)(α₂(S'')-1)$; in particular, if both $S'$ and $S''$ contain maximum arcs, then so does $S$, too.
3. If each of $S'$ and $S''$ can be covered with three maximum arcs incident with a common point, then so does $S$, too.

ISO 690:

Milazzo, L., Tuza, Z. 2007. A class of Steiner systems S(2,4,v) with arcs of extremal size. In Tatra Mountains Mathematical Publications, vol. 36, no.2, pp. 153-162. 1210-3195.

APA:

Milazzo, L., Tuza, Z. (2007). A class of Steiner systems S(2,4,v) with arcs of extremal size. Tatra Mountains Mathematical Publications, 36(2), 153-162. 1210-3195.