2018/07/22 by Nazli Besharati, Besharati, Nazli, M. Mortezaeefar +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.1807.08277
arxiv created 2018/07/22 · arxiv updated 2018/07/24
Every Steiner triple system is a uniform hypergraph. The coloring of hypergraph and its special case Steiner triple systems, STS(v), is studied extensively. But the defining set of the coloring of hypergraph even its special case STS(v), is not explored yet. We study minimum defining set and the largest minimal defining set for 3-coloring of STS(v). We determined minimum defining set and the largest minimal defining set, for all non-isomorphic STS(v), v≤ 15. Also we have found the \sf defining number for all Steiner triple systems of order v, and some lower bounds for the size of the largest minimal defining set for all Steiner triple systems of order v, for each admissible v.