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A Proof of the Hirsch Conjecture on the Polyhedron of the Shortest Route Problem

1969; Society for Industrial and Applied Mathematics; Volume: 17; Issue: 6 Linguagem: Inglês

10.1137/0117114

1095-712X

Romesh Saigal,

Transportation Planning and Optimization

Previous article Next article A Proof of the Hirsch Conjecture on the Polyhedron of the Shortest Route ProblemRomesh SaigalRomesh Saigalhttps://doi.org/10.1137/0117114PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] George B. Dantzig, Linear programming and extensions, Princeton University Press, Princeton, N.J., 1963xvi+625 MR0201189 (34:1073) 0108.33103 CrossrefGoogle Scholar[2] G. B. Dantzig, Eight unsolved problems from mathematical programming, Bull. Amer. Math. Soc., 70 (1964), 499–500 CrossrefISIGoogle Scholar[3] L. R. Ford, Jr. and , D. R. Fulkerson, Flows in networks, Princeton University Press, Princeton, N.J., 1962xii+194 MR0159700 (28:2917) 0106.34802 Google Scholar[4] Branko Grünbaum, Convex polytopes, With the cooperation of Victor Klee, M. A. Perles and G. C. Shephard. Pure and Applied Mathematics, Vol. 16, Interscience Publishers John Wiley & Sons, Inc., New York, 1967xiv+456 MR0226496 (37:2085) 0163.16603 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Advantageous Properties of Dual Transhipment PolyhedraI. Adler and S. CosaresSIAM Journal on Discrete Mathematics, Vol. 3, No. 2 | 8 August 2006AbstractPDF (1484 KB)A proof of the maximal diameter conjecture for the transportation polyhedronCybernetics, Vol. 21, No. 4 | 1 Jan 1986 Cross Ref On the Assignment PolytopeM. L. Balinski and Andrew RussakoffSIAM Review, Vol. 16, No. 4 | 18 July 2006AbstractPDF (1033 KB)On two special classes of transportation polytopesPivoting and Extension | 4 March 2009 Cross Ref The Hirsch Conjecture in Leontief Substitution SystemsRichard C. GrinoldSIAM Journal on Applied Mathematics, Vol. 21, No. 3 | 12 July 2006AbstractPDF (292 KB) Volume 17, Issue 6| 1969SIAM Journal on Applied Mathematics1017-1325 History Submitted:29 October 1968Published online:17 February 2012 InformationCopyright © 1969 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0117114Article page range:pp. 1232-1238ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics