B-coloring of $K_{2,t}$-free planar graphs

A B-coloring of a graph $G$ is a proper edge-coloring in which every $4$-cycle receives four distinct colors; let $q_B(G)$ be the minimum number of colors in such a coloring. Every graph of maximum degree $Δ$ is $K_{2,Δ+1}$-free; hence the known $2Δ$ bound for planar graphs with $Δ\ge38$ (Kong et al