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dc.contributor.authorMurty, Katta G.en_US
dc.date.accessioned2006-09-11T19:32:58Z
dc.date.available2006-09-11T19:32:58Z
dc.date.issued1973-12en_US
dc.identifier.citationMurty, Katta G.; (1973). "The graph of an abstract polytope." Mathematical Programming 4(1): 336-346. <http://hdl.handle.net/2027.42/47917>en_US
dc.identifier.issn1436-4646en_US
dc.identifier.issn0025-5610en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/47917
dc.description.abstractRecently a generalization of simple convex polytopes to combinatorial entities known as abstract polytopes has been proposed. The graph of an abstract polytope of dimension d is a regular connected graph of degree d. Given a connected regular graph Г of degree d , it is interesting to find out whether it is the graph of some abstract polytope P. We obtain necessary and sufficient conditions for this, in terms of the existence of a class of simple cycles in Г satisfying certain properties. The main result in this paper is that if a pair of simple convex polytopes or abstract polytopes have the same two-dimensional skeleton, then they are isomorphic. Every two-dimensional face of a simple convex polytope or an abstract polytope is a simple cycle in its graph. Given the graph of a simple convex polytope or an abstract polytope and the simple cycles in this graph corresponding to all its two-dimensional faces, then we show how to construct all its remaining faces. Given a regular connected graph Г and a class of simple cyles D in it, we provide necessary and sufficient conditions under which D is the class of two-dimensional faces of some abstract polytope which has Г as its graph.en_US
dc.format.extent599062 bytes
dc.format.extent3115 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypetext/plain
dc.language.isoen_US
dc.publisherSpringer-Verlag; The Mathematical Programming Societyen_US
dc.subject.otherNumerical Analysisen_US
dc.subject.otherCalculus of Variations and Optimal Controlen_US
dc.subject.otherOptimizationen_US
dc.subject.otherNumerical and Computational Methodsen_US
dc.subject.otherMathematics of Computingen_US
dc.subject.otherMathematicsen_US
dc.subject.otherMathematical Methods in Physicsen_US
dc.subject.otherCombinatoricsen_US
dc.subject.otherMathematical and Computational Physicsen_US
dc.subject.otherOperation Research/Decision Theoryen_US
dc.titleThe graph of an abstract polytopeen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelMathematicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumUniversity of Michigan, Ann Arbor, Michigan, USAen_US
dc.contributor.affiliationumcampusAnn Arboren_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/47917/1/10107_2005_Article_BF01584675.pdfen_US
dc.identifier.doihttp://dx.doi.org/10.1007/BF01584675en_US
dc.identifier.sourceMathematical Programmingen_US
dc.owningcollnameInterdisciplinary and Peer-Reviewed


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