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A pair of nonnegative integer sequences {D1 , D2} with D1 Å (d1,1 , d1,2 , . . . , d1,n1 ) and D2 Å (d2,1 , d2,2 , . . . , d2,n2 ) is a bipartite graphical sequence, if there is a bipartite graph G with degrees {D1, D2} (i.e., G has two independent vertex sets V1 Å {v1,1, v1,2, . . . , v1,n1} and V2 Å {v2,1, v2,2, . . . , v2,n2} such that di ,ji is the degree of vertex vi ,ji of G for each i Å 1, 2 and ji Å 1, 2, . . . , ni ) . In other words, {D1 , D2} is a bipartite graphical sequence if and only if there is an n1 1 n2 matrix of 0’s and 1’s having d1j1 1’s in row j1 and d2j2 1’s in column j2 . The connectivity k( {D1 , D2} ) of a bipartite graphical sequence {D1 , D2} is defined to be the maximum integer k such that there is a k-connected bipartite graph with degrees {D1 , D2} . In this paper, we present a characterization of a k-connected bipartite graphical sequence and an O (n log log n ) time algorithm, for a given bipartite graphical sequence {D1 , D2} , to construct a k( {D1 , D2} )-connected bipartite graph with degrees {D1 , D2} (n Å n1 / n2 ) . q 1997 John Wiley & Sons, Inc. Networks 29: 245–263, 1997 D1 Å (d1,1 , d1,2 , . . . , d1,n1 ) and D2 Å (d2,1 , d2,2 , . . . ,

Constructing a bipartite graph of maximum connectivity with prescribed degrees