Discussiones Mathematicae Graph Theory 29(3) (2009)
583-596
doi: 10.7151/dmgt.1466
Michael Ferrara
University of Colorado at Denver | Michael Jacobson
University of Colorado at Denver | John Schmitt
Middlebury College | Mark Siggers
Kyungpook National University |
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(K_{s,t},m,n), σ(P_{t},m,n) and σ(C_{2t},m,n).
Keywords: degree sequence, bipartite graph, potential number.
2000 Mathematics Subject Classification: 05C07, 05C35.
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Received 5 June 2008
Accepted 5 September 2008>