@Article{Zelinka2005,
author = "Zelinka, Bohdan",
title = "Independent set dominating sets in bipartite graphs",
journal = "Opuscula Math.",
year = "2005",
volume = "25",
number = "2",
pages = "345--349",
doi = "http://dx.doi.org/10.7494/OpMath.2005.25.2.345",
url = "http://dx.doi.org/10.7494/OpMath.2005.25.2.345",
abstract = "The paper continues the study of independent set dominating sets in graphs which was started by E. Sampathkumar. A subset \(D\) of the vertex set \(V(G)\) of a graph \(G\) is called a set dominating set (shortly sd-set) in \(G\), if for each set \(X \subseteq V(G)-D\) there exists a set \(Y \subseteq D\) such that the subgraph \(\langle X \cup Y\rangle\) of \(G\) induced by \(X \cup Y\) is connected. The minimum number of vertices of an sd-set in \(G\) is called the set domination number \(\gamma_s(G)\) of \(G\). An sd-set \(D\) in \(G\) such that \(|D|=\gamma_s(G)\) is called a \(\gamma_s\)-set in \(G\). In this paper we study sd-sets in bipartite graphs which are simultaneously independent. We apply the theory of hypergraphs.",
keywords = "set dominating set, set domination number, independent set, bipartite graph, multihypergraph",
issn = "1232-9274"
}