@Article{Adamus2008,
author = "Adamus, Lech and Leśniak, Edyta and Orchel, Beata",
title = "3-biplacement of bipartite graphs",
journal = "Opuscula Math.",
year = "2008",
volume = "28",
number = "3",
pages = "223--231",
doi = "http://dx.doi.org/10.7494/OpMath.2008.28.3.223",
url = "http://dx.doi.org/10.7494/OpMath.2008.28.3.223",
abstract = "Let \(G=(L,R;E)\) be a bipartite graph with color classes \(L\) and \(R\) and edge set \(E\). A set of two bijections \(\{\varphi_1 , \varphi_2\}\), \(\varphi_1 , \varphi_2 :L \cup R \to L \cup R\), is said to be a \(3\)-biplacement of \(G\) if \(\varphi_1(L)= \varphi_2(L) = L\) and \(E \cap \varphi_1^*(E)=\emptyset\), \(E \cap \varphi_2^*(E)=\emptyset\), \(\varphi_1^*(E) \cap \varphi_2^*(E)=\emptyset\), where \(\varphi_1^*\), \(\varphi_2^*\) are the maps defined on \(E\), induced by \(\varphi_1\), \(\varphi_2\), respectively. We prove that if \(|L| = p\), \(|R| = q\), \(3 \leq p \leq q\), then every graph \(G=(L,R;E)\) of size at most \(p\) has a \(3\)-biplacement.",
keywords = "bipartite graph, packing of graphs, placement, biplacement",
issn = "1232-9274"
}