Charles J. Colbourn, Melissa S. Keranen, Donald L. Kreher

The 3-GDDs of type $g^3u^2$

Başlangıç: 2015
Yayıncı: İrfan ŞİAP

A 3-GDD of type ${g^3u^2}$ exists if and only if $g$ and $u$ have the same parity, $3$ divides $u$ and $u\leq 3g$.Such a 3-GDD of type ${g^3u^2}$ is equivalent to an edge decomposition of $K_{g,g,g,u,u}$ into triangles.

PDF

___

D. Bryant, D. Horsley, Steiner triple systems with two disjoint subsystems, J. Combin. Des. 14(1) (2006) 14–24.
C. J. Colbourn, Small group divisible designs with block size three, J. Combin. Math. Combin. Comput. 14 (1993) 153–171.
C. J. Colbourn, C. A. Cusack, D. L. Kreher, Partial Steiner triple systems with equal-sized holes, J. Combin. Theory Ser. A 70(1) (1995) 56–65.
C. J. Colbourn, J. H. Dinitz (Eds.), Handbook of Combinatorial Designs, Second Edition, CRC/Chapman and Hall, Boca Raton, FL, 2007.
C. J. Colbourn, D. Hoffman, R. Rees, A new class of group divisible designs with block size three, J. Combin. Theory Ser. A 59(1) (1992) 73–89.
C. J. Colbourn, M. A. Oravas, R. S. Rees, Steiner triple systems with disjoint or intersecting subsystems, J. Combin. Des. 8(1) (2000) 58–77.
R. Rees, Uniformly resolvable pairwise balanced designs with blocksizes two and three, J. Combin. Theory Ser. A 45(2) (1987) 207-225.
R. M. Wilson, An existence theory for pairwise balanced designs. I. Composition theorems and morphisms, J. Combinatorial Theory Ser. A 13 (1972) 220–245.
R. M. Wilson, An existence theory for pairwise balanced designs. II. The structure of PBD-closed sets and the existence conjectures, J. Combinatorial Theory Ser. A 13 (1972) 246–273.