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## Enclosings of Small Cycle Systems

##### Date

2009-04-28##### Author

Newman, Nicholas

##### Type of Degree

dissertation##### Department

Mathematics and Statistics##### Metadata

Show full item record##### Abstract

In 2003 Hurd and others considered the problem of enclosing a triple system TS(v; lambda)
in a triple system TS(v + s; lambda + m), focusing on smallest possible enclosings. In
the second chapter, their result is generalized using a new proof based on a graph-theoretic
technique.
Four constructions are presented; they are exhaustive in the sense that, for each possible
congruence of the parameters v or s and m, at least one construction can be applied to obtain
an enclosing. In each construction, the value of v or s is restricted.
This naturally led to the question of whether or not a lambda-fold 4-cycle system could be
enclosed for all possible values. In the third chapter, we completely solve the enclosing
problem by construction for lambda-fold 4-cycle systems for u > 1.

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