Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Silver block intersection graphs of Steiner 2-designs   For a block design $\cal{D}$, a series of {\sf block intersection graphs}
$G_i$, or $i$-{\rm BIG}($\cal{D}$), $i=0, ..., k$ is defined in which the
vertices are the blocks of $\cal{D}$, with two vertices adjacent if and only if
the corresponding blocks intersect in exactly $i$ elements. A silver graph $G$
is defined with respect to a maximum independent set of $G$, called a {\sf
diagonal} of that graph. Let $G$ be $r$-regular and $c$ be a proper $(r +
1)$-coloring of $G$. A vertex $x$ in $G$ is said to be {\sf rainbow} with
respect to $c$ if every color appears in the closed neighborhood $N[x] = N(x)
\cup \{x\}$. Given a diagonal $I$ of $G$, a coloring $c$ is said to be silver
with respect to $I$ if every $x\in I$ is rainbow with respect to $c$. We say
$G$ is {\sf silver} if it admits a silver coloring with respect to some $I$.
  We investigate conditions for 0-{\rm BIG}($\cal{D}$) and 1-{\rm
BIG}($\cal{D}$) of Steiner systems ${\cal{D}}=S(2,k,v)$ to be silver.

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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: physics