Geodesic
Potentially H-bigraphic sequences
Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 3, pp. 583-596

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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.
Keywords: degree sequence, bipartite graph, potential number 
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Ferrara, Michael; Jacobson, Michael; Schmitt, John; Siggers, Mark. Potentially H-bigraphic sequences. Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 3, pp. 583-596. http://geodesic.mathdoc.fr/item/DMGT_2009_29_3_a9/