DOMINATING SET remains NP-complete even when instances are restricted to bipartite graphs, however, in this case VERTEX COVER is solvable in polynomial time. Consequences to VECTOR DOMINATING SET as a generalization of both are discussed.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1171, author = {Tobias Gerlach and Jochen Harant}, title = {A note on domination in bipartite graphs}, journal = {Discussiones Mathematicae Graph Theory}, volume = {22}, year = {2002}, pages = {229-231}, zbl = {1028.05075}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1171} }
Tobias Gerlach; Jochen Harant. A note on domination in bipartite graphs. Discussiones Mathematicae Graph Theory, Tome 22 (2002) pp. 229-231. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1171/
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