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