Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Determination of the size of defining set for Steiner triple systems   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}$(v)$, $v\le 15$. 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 $v$.

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The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: comp-gas