Constructing a bipartite graph of maximum connectivity with prescribed degrees
A pair of nonnegative integer sequences {l_brace}D{sub 1}, D{sub 2}{r_brace} with D{sub 1} = (d{sub 1, 1}), d{sub 1, 2}, ..., d{sub 1,n1} and D{sub 2} = (d{sub 2, 1} d{sub 2, 2}, ..., d{sub 2,n2}) is a bipartite graphical sequence, if there is a bipartite graph G with degrees {l_brace}D{sub 1}, D{sub 2}{r_brace} (i.e., G has two independent vertex sets V{sub 1} = {l_brace}v{sub 1, 1}, v{sub 1, 2}, ..., v{sub 1}, n{sub 1}{r_brace} and V{sub 2} = {l_brace}v{sub 2, 1}, v{sub 2, 2}, ..., v{sub 2,n}{sub 2}{r_brace} such that d{sub i, ji} is the degree of vertex v{sub i, ji} of G for each i = 1, 2 and ji = 1, 2, ..., n{sub i}). A bipartite graphical sequence ({l_brace}D{sub 1}, D{sub 2}) is k-connected if there is a k-connected bipartite graph with degrees {l_brace}D{sub 1}, D{sub 2}{r_brace}. The connectivity K{l_brace}D{sub 1}, D{sub 2}{r_brace} of a bipartite graphical sequence {l_brace}D{sub 1}, D{sub 2}{r_brace} is defined to be the maximum integer k such that there is a k-connected bipartite graph with degrees {l_brace}D{sub 1}, D{sub 2}{r_brace}. In this talk, we first present a characterization of a k-connected bipartite graphical sequence. Then, based on this characterization and an efficient data structure proposed by Van Emde Boas and Zijstra, we present an O(nlog log n) time algorithm, for a given bipartite graphical sequence {l_brace}D{sub 1}, D{sub 2}{r_brace}, to construct a K{l_brace}D{sub 1}, D{sub 2}{r_brace}-connected bipartite graph with degrees {l_brace}D{sub 1}, D{sub 2}{r_brace} (n = n{sub 1} + n{sub 2}).
- OSTI ID:
- 35783
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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