Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Many Triangles with Few Edges   Extremal problems concerning the number of independent sets or complete
subgraphs in a graph have been well studied in recent years. Cutler and
Radcliffe proved that among graphs with $n$ vertices and maximum degree at most
$r$, where $n = a(r+1)+b$ and $0 \le b \le r$, $aK_{r+1}\cup K_b$ has the
maximum number of complete subgraphs, answering a question of Galvin. Gan, Loh,
and Sudakov conjectured that $aK_{r+1}\cup K_b$ also maximizes the number of
complete subgraphs $K_t$ for each fixed size $t \ge 3$, and proved this for $a
= 1$. Cutler and Radcliffe proved this conjecture for $r \le 6$.
  We investigate a variant of this problem where we fix the number of edges
instead of the number of vertices. We prove that $aK_{r+1}\cup \mathcal{C}(b)$,
where $\mathcal{C}(b)$ is the colex graph on $b$ edges, maximizes the number of
triangles among graphs with $m$ edges and any fixed maximum degree $r\le 8$,
where $m = a \binom{r+1}{2} + b$ and $0 \le b < \binom{r+1}{2}$.

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The categories of this paper are: adap-org
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The categories of this paper are: eess
37
The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn