Tractable connected domination for restricted bipartite graphs

Connected domination, i.e. the problem of finding a minimum connected dominating set in a graph, was known to be $$\mathcal {NP}$$ NP -complete for chordal bipartite graphs, but to be tractable for convex bipartite graphs. In this paper, connected domination is shown to be tractable for circular- and triad-convex bipartite graphs respectively, by efficient reductions from these graphs to convex bipartite graphs.