BibTex RIS Cite

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

Year 2016, , 135 - 144, 09.08.2016
https://doi.org/10.13069/jacodesmath.52790

Abstract

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.

References

  • 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.
Year 2016, , 135 - 144, 09.08.2016
https://doi.org/10.13069/jacodesmath.52790

Abstract

References

  • 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.
There are 9 citations in total.

Details

Journal Section Articles
Authors

Charles J. Colbourn This is me

Melissa S. Keranen This is me

Donald L. Kreher This is me

Publication Date August 9, 2016
Published in Issue Year 2016

Cite

APA Colbourn, C. J., Keranen, M. S., & Kreher, D. L. (2016). The 3-GDDs of type $g^3u^2$. Journal of Algebra Combinatorics Discrete Structures and Applications, 3(3), 135-144. https://doi.org/10.13069/jacodesmath.52790
AMA Colbourn CJ, Keranen MS, Kreher DL. The 3-GDDs of type $g^3u^2$. Journal of Algebra Combinatorics Discrete Structures and Applications. August 2016;3(3):135-144. doi:10.13069/jacodesmath.52790
Chicago Colbourn, Charles J., Melissa S. Keranen, and Donald L. Kreher. “The 3-GDDs of Type $g^3u^2$”. Journal of Algebra Combinatorics Discrete Structures and Applications 3, no. 3 (August 2016): 135-44. https://doi.org/10.13069/jacodesmath.52790.
EndNote Colbourn CJ, Keranen MS, Kreher DL (August 1, 2016) The 3-GDDs of type $g^3u^2$. Journal of Algebra Combinatorics Discrete Structures and Applications 3 3 135–144.
IEEE C. J. Colbourn, M. S. Keranen, and D. L. Kreher, “The 3-GDDs of type $g^3u^2$”, Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 3, no. 3, pp. 135–144, 2016, doi: 10.13069/jacodesmath.52790.
ISNAD Colbourn, Charles J. et al. “The 3-GDDs of Type $g^3u^2$”. Journal of Algebra Combinatorics Discrete Structures and Applications 3/3 (August 2016), 135-144. https://doi.org/10.13069/jacodesmath.52790.
JAMA Colbourn CJ, Keranen MS, Kreher DL. The 3-GDDs of type $g^3u^2$. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016;3:135–144.
MLA Colbourn, Charles J. et al. “The 3-GDDs of Type $g^3u^2$”. Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 3, no. 3, 2016, pp. 135-44, doi:10.13069/jacodesmath.52790.
Vancouver Colbourn CJ, Keranen MS, Kreher DL. The 3-GDDs of type $g^3u^2$. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016;3(3):135-44.