Minimal k-arc Connected Graphs

D. R. Fulkerson, Lloyd S. Shapley

ResearchPublished 1971

A solution to the problem of determining the fewest number of arcs required in a k-arc-connected graph on n nodes by describing constructions that produce such graphs having kn/2 arcs (for kn even) or (kn + 1)/2 arcs (for kn odd). (A linear graph is k-arc-connected if it is necessary to remove at least k arcs in order to disconnect the graph.) The results of this study are applicable to the problem of synthesizing minimum cost, "k-reliable" communication networks.

Note: This paper was written in 1961 (P-2371) but never published because the authors became aware that Harary was preparing a paper solved the more general problem of determining the least number of arcs required for k-arc-connectivity. Harary's paper later appeared under the title "The Maximum Connectivity of a Graph" in Proc. Nat. Acad. Sci. 48 (1962), 1142-1146. The authors of the present paper feel that the method of proof, which is quite different from Harary's proof of the more general result, may be of some interest.

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  • Copyright: RAND Corporation
  • Availability: Available
  • Year: 1971
  • Print Format: Paperback
  • Paperback Pages: 20
  • Paperback Price: $15.00
  • DOI: https://doi.org/10.7249/P2371
  • Document Number: P-2371-1

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RAND Style Manual
Fulkerson, D. R. and Lloyd S. Shapley, Minimal k-arc Connected Graphs, RAND Corporation, P-2371-1, 1971. As of September 20, 2024: https://www.rand.org/pubs/papers/P2371-1.html
Chicago Manual of Style
Fulkerson, D. R. and Lloyd S. Shapley, Minimal k-arc Connected Graphs. Santa Monica, CA: RAND Corporation, 1971. https://www.rand.org/pubs/papers/P2371-1.html. Also available in print form.
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