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    On balanced incomplete block designs with specified weak chromatic number

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    A weak cc-colouring of a balanced incomplete block design (BIBD) is a colouring of the points of the design with cc colours in such a way that no block of the design has all of its vertices receive the same colour. A BIBD is said to be weakly cc-chromatic if cc is the smallest number of colours with which the design can be weakly coloured. In this paper we show that for all c≥2c \geq 2 and k≥3k \geq 3 with (c,k)≠(2,3)(c,k) \neq (2,3), the obvious necessary conditions for the existence of a (v,k,λ)(v,k,\lambda)-BIBD are asymptotically sufficient for the existence of a weakly cc-chromatic (v,k,λ)(v,k,\lambda)-BIBD.Comment: 26 pages, 0 figure
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