Distinguishing Chromatic Numbers of Bipartite Graphs - Laflamme, C.; Seyffarth, K. (The Electronic Journal of Combinatorics, 2009)
Extending the work of K.L. Collins and A.N. Trenk, we characterize connected bipartite graphs with large distinguishing chromatic number. In particular, if $G$ is a connected bipartite graph with maximum degree $Δ ≥ 3$, then $χ_D(G)≤ 2Δ -2$ whenever $G ot\cong K_{Δ-1,Δ}$, $K_{Δ,Δ}$.