Let G = (L,R;E) be a bipartite graph such that V(G) = L∪R, |L| = p and |R| = q. G is called (p,q)-tree if G is connected and |E(G)| = p+q-1. Let G = (L,R;E) and H = (L',R';E') be two (p,q)-tree. A bijection f:L ∪ R → L' ∪ R' is said to be a biplacement of G and H if f(L) = L' and f(x)f(y) ∉ E' for every edge xy of G. A biplacement of G and its copy is called 2-placement of G. A bipartite graph G is 2-placeable if G has a 2-placement. In this paper we give all (p,q)-trees which are not 2-placeable.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1183,
author = {Beata Orchel},
title = {2-placement of (p,q)-trees},
journal = {Discussiones Mathematicae Graph Theory},
volume = {23},
year = {2003},
pages = {23-36},
zbl = {1051.05052},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1183}
}
Beata Orchel. 2-placement of (p,q)-trees. Discussiones Mathematicae Graph Theory, Tome 23 (2003) pp. 23-36. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1183/
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