  In this short note, we extend the result of Galluccio, Goddyn, and Hell,
which states that graphs of large girth excluding a minor are nearly bipartite.
We also prove a similar result for the oriented chromatic number, from which
follows in particular that graphs of large girth excluding a minor have
oriented chromatic number at most $5$, and for the $p$th chromatic number
$\chi_p$, from which follows in particular that graphs $G$ of large girth
excluding a minor have $\chi_p(G)\leq p+2$.
