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Perfect Partitions of Some (0,1)-Matrices

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Author: Soosiah, Jeffrey
Advisor: Yu, Gexin
Committee Members: Vinroot, C. Ryan; Mao, Weizhen
Issued Date: 7/13/2012
Subjects: Combinatorics
Math
Graph Theory
Matrices
Partition
URI: http://hdl.handle.net/10288/16710
Description: 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.
Degree: Bachelors of Science in Mathematics


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