Luther, Robert D. (2016) Equitably coloured balanced incomplete block designs. Masters thesis, Memorial University of Newfoundland.
- Accepted Version
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In this thesis we determine necessary and sufficient conditions for the existence of an equitably ℓ-colourable balanced incomplete block design for any positive integer ℓ > 2. In particular, we present a method for constructing non-trivial equitably ℓ-colourable BIBDs and prove that these designs are the only non-trivial equitably ℓ-colourable BIBDs that exist. We also observe that every equitable ℓ-colouring of a BIBD yields both an equalised ℓ-colouring and a proper 2-colouring of the same BIBD. We also discuss generalisations of these concepts including open questions for further research. The main results presented in this thesis also appear in .
|Item Type:||Thesis (Masters)|
|Additional Information:||Includes bibliographical references (page 18).|
|Keywords:||Designs, colourings, combinatorics|
|Department(s):||Science, Faculty of > Mathematics and Statistics|
|Library of Congress Subject Heading:||Incomplete block designs; Graph coloring; Set theory|
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