Weak and Block-Equitable Colourings in Uniform Group Divisible Designs and Maximum Packings
By
Andrea C. Burgess
Kettled twice. Extra chewy, extra trustworthy.
Summary
This article presents a mathematical study of colourings in uniform group divisible designs and maximum packings. It defines weak c-colourings (assigning colours to points so no block is monochromatic) and block-equitable colourings (where each block has a balanced distribution of colours). The research explores theoretical properties and classifications of these colouring types within specific combinatorial design structures.
Key quotes
· 2 pulledA weak c-colouring of a design is an assignment of colours to its points from a set of c available colours, such that there are no monochromatic blocks.
A colouring of a design is block-equitable, if for each block, the number of points coloured with any available pair of colours differ by at most one.
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