Electronic Theses and Dissertations

# C4-Factorizations with Two Associate Classes

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dc.contributor.authorTiemeyer, Michael
dc.date.accessioned2010-04-29T18:16:00Z
dc.date.available2010-04-29T18:16:00Z
dc.date.issued2010-04-29T18:16:00Z
dc.identifier.urihttp://hdl.handle.net/10415/2127
dc.description.abstractLet $K = K(a,p;\lambda_{1},\lambda_{2})$ be the multigraph with: the number of vertices in each part equal to $a$; the number of parts equal to $p$; the number of edges joining any two vertices of the same part equal to $\lambda_{1}$; and the number of edges joining any two vertices of different parts equal to $\lambda_{2}$. This graph was of interest to Bose and Shimamoto in their study of group divisible designs with two associate classes \cite{bose}. Necessary and sufficient conditions for the existence of $z$-cycle decompositions of this graph have been found when $z \in \{3,4\}$\cite{fu1,fu2}. The existence of resolvable 4-cycle decompositions of $K$ has been settled when $a$ is even \cite{br}, but the odd case is much more difficult. In this paper, necessary and sufficient conditions for the existence of a $C_{4}$-factorization of $K(a,p;\lambda_{1},\lambda_{2})$ are found when $a \equiv 1 (mod\;4)$ and $\lambda_{1}$ is even, and all cases with one exception have been solved when $\lambda_{1}$ is odd.en
dc.rightsEMBARGO_NOT_AUBURNen
dc.subjectMathematics and Statisticsen
dc.titleC4-Factorizations with Two Associate Classesen
dc.typedissertationen
dc.embargo.lengthMONTHS_WITHHELD:6en_US
dc.embargo.statusEMBARGOEDen_US
dc.embargo.enddate2010-10-29en_US