Abstract
Let Meta(H > T, λ) denote the set of all integers v such that there exists a (H > T)-GM λ (v). In this paper, the set Meta(H > T, λ) will be completely determined for the following 21 pairs (H, T) = (H 1, P 2), (H 2, 2P 2), (H 3, P 3) and (H 4, P 4), where \({P_2 \subset H_1 \subseteq K_4, H_2 \in \{K_4, C_4, K_3+e, P_4\} = {\mathcal {H}}, H_3 \in {\mathcal {H}} \cup \{K_3, K_{1,3} \}}\) and \({H_4 \in \{K_4, C_4\}}\) .
Similar content being viewed by others
References
Baker C.A.: Extended skolem seqences. J. Combin. Designs 3, 363–379 (1995)
Billington, E.J., Dancer, K.A.: The metamorphosis of designs with block size four: a survey and the final case. Congressus Numerantium 164, 129–151 (2003)
Chang Y.X, Lo Faro G., Tripodi A.: The spectrum of Meta(K 4 − e > K 3 + e, λ) with any λ. Utilitas Math 72, 3–22 (2007)
Colbourn, C.J., Dinitz, J.H. (eds.): Handbook of Combinatorial Designs, 2nd edn. CRC Press, Boca Raton (2006)
Kücükcifci S., Lindner C.C.: The metamorphosis of λ-fold block designs with block size four into λ-fold kite designs. J. Combin. Math. Combin. Comput. 40, 241–252 (2002)
Kücükcifci S., Lindner C.C.: The metamorphosis of λ-fold block designs with block size four into λ-fold (K 4 − e)-systems, λ ≥ 2. Utilitas Math. 63, 239–254 (2003)
Lindner C.C., Rosa A.: The metamorphosis of λ-fold block designs with block size four into λ-fold triple systems. J. Stat. Plann. Infer. 106(1–2), 69–76 (2002)
Lindner C.C., Rosa A.: The metamorphosis of λ-fold block designs with block size four into (K 4 − e)-designs. Utilitas Math. 6, 33–46 (2002)
Lindner, C.C., Rodger, C.A.: Design Theory, CRC Press Series on Discrete Mathematics and its Application. CRC Press, Boca Raton (1997)
Lindner C.C., Tripodi A.: The metamorphosis of (K 4 − e)-designs into maximum packings of λ K n with 4-cycles. Ars Combinatoria 75, 333–349 (2005)
Lindner C.C., Tripodi A.: The metamorphosis of λ-fold (K 4 − e)-designs into maximum packings of λ K n with 4-cycles, λ ≥ 2. J. Stat. Plann. Infer. 138(11), 3316–3325 (2008)
Lindner, C.C., Street, A.P.: The metamorphosis of λ-fold block designs with block size four into λ-fold 4-cycle systems. Bull. Inst. Combin. Appl. 28, 7–18. Corrigendum, Bull. Inst. Combin. Appl. 29, 88 (2000)
Lo Faro, G., Lindner, C.C., Tripodi, A.: The metamorphosis of λ-fold kite systems into maximum packings of λ K n with triangles. JCMCC 56, 171–189 (2006)
Lo Faro G., Tripodi A.: The spectrum of Meta(K 3 + e > P 4, λ) and Meta(K 3 + e > H 4, λ) with any λ. Discret. Math. 309, 354–362 (2009)
Zhang Y., Hou Y., Kang Q.: The spectrum of Meta(H > T, λ) for all subgraphs H and T of K 4 II. Bull. Inst. Combin. Appl. 59, 46–70 (2010)
Hou, Y., Zhang, Y., Yuan, L., Kang, Q.: The spectrum of Meta(H > T, λ) for all subgraphs H and T of K 4 III, submitted (2010)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yuan, L., Zhang, Y., Hou, Y. et al. The Spectrum Meta(H > T, λ) for Some Subgraphs H and T of K 4 . Graphs and Combinatorics 30, 1301–1318 (2014). https://doi.org/10.1007/s00373-013-1332-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00373-013-1332-x