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Independent sets in Steiner triple systems. (English) Zbl 1069.05009
A set of elements in a Steiner triple system is independent when no three lie in a block. The number of independent sets with few elements (at most 8) is determined in terms of numbers of occurrences of small configurations of blocks. These numbers in turn establish that every Steiner triple system of order 21 has an independent set of size at least 8, and hence that each is 4-colourable.

MSC:
05B07 Triple systems
Keywords:
colouring
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