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Perfect Partitions of Some (0,1)-Matrices
Soosiah, Jeffrey
Soosiah, Jeffrey
Abstract
For a given regular bipartite graph G, can we partition the set of all perfect matchings of G into subsets such that each subset gives a 1-factorization of G? Or equivalently, given a (0; 1)-matrix A and the set PA of permutation matrices componentwise less than A, can we partition PA into subsets so that the matrix sum of elements in each subset is A? If so, we say the graph G or the matrix A has a perfect partition. We focus our attention on a class of regular bipartite graphs, and show the existence of perfect partitions for two particular regular bipartite graphs of the class.
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Thesis is part of Honors ETD pilot project, 2008-2013. Migrated from Dspace in 2016.
Date
2012-07-13
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Combinatorics, Math, Graph Theory, Matrices, Partition
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Mathematics