The existence of edge-coloured block designs with block size four is studied for all nonisomorphic colourings of the edges of a K4. There are 25 nonisomorphic edge-coloured K4's; for each, we examine the existence of edge-coloured designs with the minimum possible index. Uniform cases lead to block designs, perpendicular arrays, nested Steiner triple systems, idempotent Schroeder quasigroups, and other combinatorial objects.
- AMS (1980) subject classification: Primary 05B30
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics