Domination in bipartite graphs and in their complements

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 dc.contributor.author Zelinka, Bohdan dc.date.accessioned 2015-10-26 dc.date.available 2015-10-26 dc.date.issued 2015 dc.date.issued 2003 dc.identifier.issn 0370-2693 dc.identifier.issn 0011-4642 dc.identifier.uri https://dspace.tul.cz/handle/15240/16326 dc.identifier.uri https://dspace.tul.cz/handle/15240/13327 dc.description.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. en dc.format text dc.format text dc.language.iso en dc.language.iso en dc.publisher Elsevier dc.publisher Technical university of Liberec, Czech Republic en dc.publisher Technická Univerzita v Liberci cs dc.relation.ispartof Czechoslovak Mathematical Journal en dc.source j-scopus dc.source j-wok dc.source j-scopus dc.subject bipartite graph en dc.subject complement of a graph en dc.subject domatic number en dc.title Domination in bipartite graphs and in their complements en dc.type Article dc.type Article dc.identifier.doi 10.1016/j.physletb.2015.03.056 dc.identifier.doi 10.1023/A:1026266816053 local.relation.volume 53 local.relation.issue 2 local.identifier.wok 353892000039 local.identifier.scopus 2-s2.0-84927722335 local.identifier.scopus 2-s2.0-0041738904 local.faculty Faculty of Sciences, Humanities and Education local.citation.spage 241 local.citation.epage 259 local.citation.epage 247 local.identifier.coden PYLBA local.department Department of Physics local.access οpen
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