Group Divisible Designs with Two Associate Classes:n=2 orm=2

Decompositions of complete graphs into triangles and Hamilton cycles

“…There is a paper by Dejter et al [11] which is concerned with the total number of triangles in 2-factorizations of K n . Finally, there is a paper by Fu and Rodger [13] in which necessary and sufficient conditions for a decomposition of the -fold complete graph into triangles and 1-factors are proved.…”

Odd and even group divisible designs with two groups and block size four

“…So bi comes with j in blocks six more times for a total of 21. For i and bi, the replication number r of bi in one copy of Y1; : : : ; Y8-a TS (8,3,6), is r = 6(8 − 1)=2 = 21. So 2 = 21.…”

“…The problem of necessary and su cient conditions for m = 2 or n = 2, and block size 3, was established in [6]. The purpose of this note is to begin to establish similar results for block size 4, and for this note, we concentrate on m = 2, v = 2n and k = 4 throughout.…”

Group divisible designs with block size four and two groups

“…In [7] the existence problem was settled for GDDs with first and second associates with block size k = 3 and with m groups each of size n with m, n 3. The problem of necessary and sufficient conditions for m = 2 or n = 2, and block size three, was established in [6]. Unless otherwise stated, m = 2 is assumed from now on.…”

“…Designs of the type discussed here have been called both GDDs and group divisible PBIBDs (partially balanced incomplete block designs) and we refer the reader to [6,14] and the references therein. When 1 = 0 and 2 = 1 then exponential notation k − GDD(n m ) is usually used for GDD with m groups of size n and block size k [12].…”