On balanced incomplete block designs with specified weak chromatic number

Authors:
Daniel Horsley;David A. Pike
Affiliations:
School of Mathematical Sciences, Monash University, Vic 3800, Australia;Department of Mathematics and Statistics, Memorial University of Newfoundland, St. Johns, NL, A1C 5S7, Canada
Venue:
Journal of Combinatorial Theory Series A
Year:
2014

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Abstract

A weak c-colouring of a balanced incomplete block design (BIBD) is a colouring of the points of the design with c 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 c-chromatic if c is the smallest number of colours with which the design can be weakly coloured. In this paper we show that for all c=2 and k=3 with (c,k)(2,3), the obvious necessary conditions for the existence of a (v,k,@l)-BIBD are asymptotically sufficient for the existence of a weakly c-chromatic (v,k,@l)-BIBD.