We extend the notion of a potentially H-graphic sequence as follows. Let A and B be nonnegative integer sequences. The sequence pair S = (A,B) is said to be bigraphic if there is some bipartite graph G = (X ∪ Y,E) such that A and B are the degrees of the vertices in X and Y, respectively. If S is a bigraphic pair, let σ(S) denote the sum of the terms in A. Given a bigraphic pair S, and a fixed bipartite graph H, we say that S is potentially H-bigraphic if there is some realization of S containing H as a subgraph. We define σ(H,m,n) to be the minimum integer k such that every bigraphic pair S = (A,B) with |A| = m, |B| = n and σ(S) ≥ k is potentially H-bigraphic. In this paper, we determine , σ(Pₜ,m,n) and .
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1466,
author = {Michael Ferrara and Michael Jacobson and John Schmitt and Mark Siggers},
title = {Potentially H-bigraphic sequences},
journal = {Discussiones Mathematicae Graph Theory},
volume = {29},
year = {2009},
pages = {583-596},
zbl = {1194.05022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1466}
}
Michael Ferrara; Michael Jacobson; John Schmitt; Mark Siggers. Potentially H-bigraphic sequences. Discussiones Mathematicae Graph Theory, Tome 29 (2009) pp. 583-596. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1466/
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