Geodesic
Domination in bipartite graphs and in their complements
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 2, pp. 241-247

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

The domatic numbers of a graph $G$ and of its complement $\bar{G}$ were studied by J. E. Dunbar, T. W. Haynes and M. A. Henning. They suggested four open problems. We will solve the following ones: Characterize bipartite graphs $G$ having $d(G) = d(\bar{G})$. Further, we will present a partial solution to the problem: Is it true that if $G$ is a graph satisfying $d(G) = d(\bar{G})$, then $\gamma (G) = \gamma (\bar{G})$? Finally, we prove an existence theorem concerning the total domatic number of a graph and of its complement.
Classification : 05C69
Keywords: bipartite graph; complement of a graph; domatic number 
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     title = {Domination in bipartite graphs and in their complements},
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Zelinka, Bohdan. Domination in bipartite graphs and in their complements. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 2, pp. 241-247. http://geodesic.mathdoc.fr/item/CMJ_2003__53_2_a1/