Distinguishing Chromatic Numbers of Bipartite Graphs
Claude Laflamme, Karen Seyffarth · 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 $\Delta \geq 3$, then $\chi_D(G)\leq 2\Delta -2$ whenever $G ot\cong K_{\Delta-1,\Delta}$, $K_{\Delta,\Delta}$.