A family of resolvable regular graph designs. (English) Zbl 0855.62062
Summary: A regular graph design \(RGD (v,k;r)\) is a design on \(v\) points with blocks of size \(k\) and constant replication number \(r\), such that any two points belong to either \( \lambda_1\) or \(\lambda_1 + 1\) common blocks, for some constant \(\lambda_1\). We investigate resolvable regular graph designs with block size 4. In particular we determine the parameters for which such designs exist, for \(v \leq 16\).
References:
| [1] | Brown, R. B., Nonexistence of a regular graph design with \(v = 17\) and \(k = 6\), Discrete Math., 68, 315-318 (1988) · Zbl 0644.05009 |
| [2] | Cheng, C. S., Optimal properties of balanced incomplete block and other designs, (Coding Theory and Design Theory (1990), Springer: Springer Berlin), 54-64, Part II · Zbl 0702.62067 |
| [3] | Constantine, G. M., On the optimality of block designs, Ann. Inst. Statist. Math., 38, 161-174 (1986) · Zbl 0588.62123 |
| [4] | Elenbogen, B. S.; Maxim, B. R., Scheduling a bridge club (a case study in discrete optimization), Math. Mag., 65, 18-26 (1992) · Zbl 0757.90064 |
| [5] | Hall, M., Combinatorial Theory, ((1986), Wiley: Wiley New York) · Zbl 0588.05001 |
| [6] | John, J. A.; Mitchell, T. J., Optimal incomplete block designs, J. Roy. Statist. Soc., 39B, 39-43 (1977) · Zbl 0354.05015 |
| [7] | Royle, G. F.; Wallis, W. D., Constructing bridge club designs, Bull. ICA, 11, 122-125 (1994) · Zbl 0811.90047 |
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