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Published online by Cambridge University Press: 04 November 2009
Abstract
A Rosa triple system is a triple system of order congruent to 2 modulo 3 whose chromatic index is minimum, having the largest possible number of maximum parallel classes in such a block colouring. The existence of Rosa triple systems is settled completely. Together with known results on Kirkman, Hanani, and almost resolvable twofold triple systems, the existence of Rosa triple systems is used to settle completely the existence of triple systems with minimum chromatic index.
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