Facebook Instagram Twitter RSS Feed Back to top on side

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.