Domination in bipartite graphs and in their complements

Bohdan Zelinka

Czechoslovak Mathematical Journal (2003)

  • Volume: 53, Issue: 2, page 241-247
  • ISSN: 0011-4642

Abstract

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The domatic numbers of a graph G and of its complement 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 ( G ¯ ) . Further, we will present a partial solution to the problem: Is it true that if G is a graph satisfying d ( G ) = d ( G ¯ ) , then γ ( G ) = γ ( G ¯ ) ? Finally, we prove an existence theorem concerning the total domatic number of a graph and of its complement.

How to cite

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Zelinka, Bohdan. "Domination in bipartite graphs and in their complements." Czechoslovak Mathematical Journal 53.2 (2003): 241-247. <http://eudml.org/doc/30773>.

@article{Zelinka2003,
abstract = {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.},
author = {Zelinka, Bohdan},
journal = {Czechoslovak Mathematical Journal},
keywords = {bipartite graph; complement of a graph; domatic number; bipartite graph; complement of a graph; domatic number},
language = {eng},
number = {2},
pages = {241-247},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Domination in bipartite graphs and in their complements},
url = {http://eudml.org/doc/30773},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Zelinka, Bohdan
TI - Domination in bipartite graphs and in their complements
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 2
SP - 241
EP - 247
AB - 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.
LA - eng
KW - bipartite graph; complement of a graph; domatic number; bipartite graph; complement of a graph; domatic number
UR - http://eudml.org/doc/30773
ER -

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