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We study open colorings in certain classes of hereditary Lindel\"{o}f($\mathsf{HL}$) spaces and submetrizable spaces. In particular, we show thatthe definible version for the Open Graph Axiom ($\mathsf{OGA}$) holds for theclass of $\mathsf{HL}$ strong Choquet submetrizable spaces extending awell-known result of Feng. Furthermore, we show the consistency of the OpenGraph Axiom for regular spaces that have countable spread and it's square alsohas it, reaching closer to a well known conjecture of Todor\v{c}evi\'{c}: "Itis consistent that all regular spaces with countable spread satisfy$\mathsf{OGA}$".

$\mathsf{SOCA}$ and $\mathsf{OGA}$ for $\mathsf{HL}$ spaces with strong properties