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2016

Cayley Graphs

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Two Problems Of Gerhard Ringel, Adrian Pastine Jan 2016

Two Problems Of Gerhard Ringel, Adrian Pastine

Dissertations, Master's Theses and Master's Reports

Gerhard Ringel was an Austrian Mathematician, and is regarded as one of the most influential graph theorists of the twentieth century. This work deals with two problems that arose from Ringel's research: the Hamilton-Waterloo Problem, and the problem of R-Sequences.

The Hamilton-Waterloo Problem (HWP) in the case of Cm-factors and Cn-factors asks whether Kv, where v is odd (or Kv-F, where F is a 1-factor and v is even), can be decomposed into r copies of a 2-factor made entirely of m-cycles and s copies of a 2-factor made entirely of …