Domination in bipartite graphs and in their complements
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Date
2015, 2003
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Technical university of Liberec, Czech Republic
Technická Univerzita v Liberci
Technical university of Liberec, Czech Republic
Technická Univerzita v Liberci
Abstract
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(Ḡ). Further, we will present a partial solution to the problem: Is it true that if G is a graph satisfying d(G) = d(Ḡ), then γ(G) = γ(Ḡ)? Finally, we prove an existence theorem concerning the total domatic number of a graph and of its complement.
Description
Subject(s)
bipartite graph, complement of a graph, domatic number
Citation
ISSN
0370-2693
0011-4642
0011-4642