Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal Limit Theorems in Graph Coloring Problems With Connections to
  Extremal Combinatorics   This paper proves limit theorems for the number of monochromatic edges in
uniform random colorings of general random graphs. These can be seen as
generalizations of the birthday problem (what is the chance that there are two
friends with the same birthday?). It is shown that if the number of colors
grows to infinity, the asymptotic distribution is either a Poisson mixture or a
Normal depending solely on the limiting behavior of the ratio of the number of
edges in the graph and the number of colors. This result holds for any graph
sequence, deterministic or random. On the other hand, when the number of colors
is fixed, a necessary and sufficient condition for asymptotic normality is
determined. Finally, using some results from the emerging theory of dense graph
limits, the asymptotic (non-normal) distribution is characterized for any
converging sequence of dense graphs. The proofs are based on moment
calculations which relate to the results of Erd\H os and Alon on extremal
subgraph counts. As a consequence, a simpler proof of a result of Alon,
estimating the number of isomorphic copies of a cycle of given length in graphs
with a fixed number of edges, is presented.

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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th