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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.
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...
The set of all non-increasing nonnegative integer sequences () is denoted by . A sequence is said to be graphic if it is the degree sequence of a simple graph on vertices, and such a graph is called a realization of . The set of all graphic sequences in is denoted by . A graphical sequence is potentially -graphical if there is a realization of containing as a subgraph, while is forcibly -graphical if every realization of contains as a subgraph. Let denote a complete...
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