The fully indecomposable matrix and its associated bipartite graph - an investigation of combinatorial and structural properties

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dc.contributor.advisorSinkhorn, Richard D.
dc.contributor.committeeMemberBrand, Louis
dc.contributor.committeeMemberKnopp, Paul J.
dc.contributor.committeeMemberEtgen, Garrett J.
dc.contributor.committeeMemberWhitaker, Thomas N.
dc.creatorRoberts, Edwin Joseph
dc.date.accessioned2022-06-22T13:40:20Z
dc.date.available2022-06-22T13:40:20Z
dc.date.issued1970
dc.description.abstractFor any nxn (0,1) matrix A , a correspondence is established between A and a certain bigraph G . Equivalences between various concepts pertaining to A and G , respectively, are demonstrated. It is shown that if A is fully indecomposable, then G is 2-connected. A method is developed for reducing a bigraph G of a nearly decomposable matrix to a strictly smaller biqraph G' , which is also associated with a nearly decomposable matrix A' . This result is used to completely characterize the fully indecomposable matrices in terms of their bigraphs and leads to a lower-bound estimate for the permanent function on this class of matrices. Finally, the characterization theorem is shown to be relevant to the problems of (1) finding an upper-bound estimate for the permanent and (2) of determining the structure of the class of nearly decomposable matrices. Some partial results along these lines are given.
dc.description.departmentMathematics, Department of
dc.format.digitalOriginreformatted digital
dc.format.mimetypeapplication/pdf
dc.identifier.other13673477
dc.identifier.urihttps://hdl.handle.net/10657/9721
dc.language.isoen
dc.rightsThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. Section 107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.
dc.titleThe fully indecomposable matrix and its associated bipartite graph - an investigation of combinatorial and structural properties
dc.type.dcmiText
dc.type.genreThesis
thesis.degree.collegeCollege of Arts and Sciences
thesis.degree.departmentMathematics, Department of
thesis.degree.disciplineMathematics
thesis.degree.grantorUniversity of Houston
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy

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