Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximizing the size of the giant   We consider two classes of random graphs: $(a)$ Poissonian random graphs in
which the $n$ vertices in the graph have i.i.d.\ weights distributed as $X$,
where $\mathbb{E}(X) = \mu$. Edges are added according to a product measure and
the probability that a vertex of weight $x$ shares and edge with a vertex of
weight $y$ is given by $1-e^{-xy/(\mu n)}$. $(b)$ A thinned configuration model
in which we create a ground-graph in which the $n$ vertices have i.i.d.\
ground-degrees, distributed as $D$, with $\mathbb{E}(D) = \mu$. The graph of
interest is obtained by deleting edges independently with probability $1-p$.
  In both models the fraction of vertices in the largest connected component
converges in probability to a constant $1-q$, where $q$ depends on $X$ or $D$
and $p$.
  We investigate for which distributions $X$ and $D$ with given $\mu$ and $p$,
$1-q$ is maximized. We show that in the class of Poissonian random graphs, $X$
should have all its mass at 0 and one other real, which can be explicitly
determined. For the thinned configuration model $D$ should have all its mass at
0 and two subsequent positive integers.

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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: eess