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k-optimal Partitions of a Directed Graph

โœ Scribed by Berge, C.

Book ID
122063396
Publisher
Elsevier Science
Year
1982
Tongue
English
Weight
345 KB
Volume
3
Category
Article
ISSN
0195-6698

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Let D = (V1, V2; A) be a directed bipartite graph with II/11 = 11/21 = n ~> 2. Suppose that do(x) + do(y) >~ 3n + 1 for all xe I/1 and ye V2. Then D contains two vertex-disjoint directed cycles of lengths 2nl and 2n2, respectively, for any positive integer partition n = n~ + n2. Moreover, the condit