  Hu and Li investigate the signed graph version of Erd$\ddot{\mathrm{o}}$s
problem: Is there a constant $c$ such that every signed planar graph without
$k$-cycles, where $4\leq k\leq c$, is $3$-colorable and prove that each signed
planar graph without cycles of length from 4 to 8 is 3-colorable. We give a
very short and simple proof of this result and improve it, based on a recent
observation.
