Colouring problems for symmetric configurations with block size 3

Erskine, Grahame; Griggs, Terry and Širáň, Jozef (2021). Colouring problems for symmetric configurations with block size 3. Journal of Combinatorial Designs, 29(6) pp. 397–423.



The study of symmetric configurations v3 with block size 3 has a long and rich history. In this paper we consider two colouring problems which arise naturally in the study of these structures. The first of these is weak colouring, in which no block is monochromatic; the second is strong colouring, in which every block is multichromatic. The former has been studied before in relation to blocking sets. Results are proved on the possible sizes of blocking sets and we begin the investigation of strong colourings. We also show that the known 213 and 223 configurations without a blocking set are unique and make a complete enumeration of all nonisomorphic 203 configurations. We discuss the concept of connectivity in relation to symmetric configurations and complete the determination of the spectrum of 2‐connected symmetric configurations without a blocking set. A number of open problems are presented.

Viewing alternatives

Download history


Public Attention

Altmetrics from Altmetric

Number of Citations

Citations from Dimensions

Item Actions