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

In: Tatra Mountains Mathematical Publications, vol. 36, no. 2
Lorenzo Milazzo - Zsolt Tuza
Detaily:
Rok, strany: 2007, 153 - 162
Kľúčové slová:
independent set, Steiner system, maximum arc, edge decomposition, mixed hypergraph
O článku:
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. 2(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.
Ako citovať:
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.