Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chromatic bounds for some classes of $2K_2$-free graphs   A hereditary class $\mathcal{G}$ of graphs is $\chi$-bounded if there is a
$\chi$-binding function, say $f$ such that $\chi(G) \leq f(\omega(G))$, for
every $G \in \cal{G}$, where $\chi(G)$ ($\omega(G)$) denote the chromatic
(clique) number of $G$. It is known that for every $2K_2$-free graph $G$,
$\chi(G) \leq \binom{\omega(G)+1}{2}$, and the class of ($2K_2, 3K_1$)-free
graphs does not admit a linear $\chi$-binding function. In this paper, we are
interested in classes of $2K_2$-free graphs that admit a linear $\chi$-binding
function. We show that the class of ($2K_2, H$)-free graphs, where $H\in
\{K_1+P_4, K_1+C_4, \overline{P_2\cup P_3}, HVN, K_5-e, K_5\}$ admits a linear
$\chi$-binding function. Also, we show that some superclasses of $2K_2$-free
graphs are $\chi$-bounded.

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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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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: nlin
13
The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci