Cover: Minimal k-arc Connected Graphs

Minimal k-arc Connected Graphs

Published 1971

by D. R. Fulkerson, Lloyd S. Shapley

Download

Download Free Electronic Document

FormatFile SizeNotes
PDF file 8.4 MB

Use Adobe Acrobat Reader version 10 or higher for the best experience.

Purchase

Purchase Print Copy

 Format Price
Add to Cart Paperback20 pages $15.00

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.

This report is part of the RAND paper series. The paper was a product of RAND from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.

This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit www.rand.org/pubs/permissions.

RAND is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.