Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Chudnovsky-Seymour-Sullivan Conjecture on Cycles in Triangle-free
  Digraphs   For a simple digraph $G$ without directed triangles or digons, let $\beta(G)$
be the size of the smallest subset $X \subseteq E(G)$ such that $G\setminus X$
has no directed cycles, and let $\gamma(G)$ be the number of unordered pairs of
nonadjacent vertices in $G$. In 2008, Chudnovsky, Seymour, and Sullivan showed
that $\beta (G) \le \gamma(G)$, and conjectured that $\beta (G) \le
\gamma(G)/2$. Recently, Dunkum, Hamburger, and P\'or proved that $\beta (G) \le
0.88 \gamma(G)$. In this note, we prove that $\beta (G) \le 0.8616 \gamma(G)$.

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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci