By C.J. Colbourn, Rudolf Mathon
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Extra resources for Combinatorial Design Theory
N ~3 (mod 4). Then '/z (n-1) is odd. Case 2iiibl. G has the form of (i) of Figure 3. D. J. W . h(n+l) edges of G. Consider first the case when %(n+l) colours are used on the edges of G. Then G has no loops and each edge has a different colour. , . where, for O_
Mn), where IGi = mi. Of course, where there is no danger of confusion, the type of the K-GDD will be represented as a multiset using the “exponential” notation. There are some useful PBDs derived from TDs and finite planes, and we shall present some fundamental lemmas below before proceeding to the next section. For the most part, the proofs of these lemmas can be found in [l]. E. Bennett 46 We have the following obvious “Direct Product’’ construction. 7: Let K be a set of positive integers and suppose u , u E B ( K ) .
Consider first the case when %(n+l) colours are used on the edges of G. Then G has no loops and each edge has a different colour. , . where, for O_