Equitably coloured balanced incomplete block designs

Luther, Robert D. (2016) Equitably coloured balanced incomplete block designs. Masters thesis, Memorial University of Newfoundland.

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Abstract

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 [7].

Item Type: Thesis (Masters)
URI: http://research.library.mun.ca/id/eprint/11948
Item ID: 11948
Additional Information: Includes bibliographical references (page 18).
Keywords: Designs, colourings, combinatorics
Department(s): Science, Faculty of > Mathematics and Statistics
Date: March 2016
Date Type: Submission
Library of Congress Subject Heading: Incomplete block designs; Graph coloring; Set theory

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