Electronic Theses and Dissertations

# The Complete Solution of the Intersection Problem for Maximum Packings of K_n with Triples

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dc.contributor.authorHolmes, Amber
dc.date.accessioned2018-07-03T17:58:54Z
dc.date.available2018-07-03T17:58:54Z
dc.date.issued2018-07-03
dc.identifier.urihttp://hdl.handle.net/10415/6266
dc.description.abstractIn the late 1980's the intersection problem for maximum packings of K_n with triples was solved by Hoffman, Lindner, and Quattrocchi. Their combined results showed that for any n = i mod(6) such that i in { 0, 2, 4, 5} the intersection spectrum is I(n)={0, 1, ..., x}\{x-1, x-2, x-3, x-5} where x is the size of a maximum packing. Each result was formed when all leaves are the same. However, in this thesis we show that if the leaves are not necessarily the same we can eliminate the exceptions {x-1, x-2, x-3, x-5} of the given results. We show that the intersection spectrum for n = i mod(6) such that i in {4, 5} is I(n)={0, 1, ..., x} where x is the size of a maximum packing and I(n)={0, 1, ..., x}\{x-1} for n = j mod(6) such that j in { 0, 2} and n (not equal to) 8; I(8)={0, 1, 2, 3, 4, 5, 8}.en_US
dc.rightsEMBARGO_NOT_AUBURNen_US
dc.subjectMathematics and Statisticsen_US
dc.titleThe Complete Solution of the Intersection Problem for Maximum Packings of K_n with Triplesen_US
dc.typePhD Dissertationen_US
dc.embargo.lengthMONTHS_WITHHELD:13en_US
dc.embargo.statusEMBARGOEDen_US
dc.embargo.enddate2019-08-03en_US
dc.contributor.committeeHoffman, Dean
dc.contributor.committeeRodger, Chris
dc.contributor.committeeRosa, Alexander
dc.contributor.committeeJohnson, Pete