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Embeddings of \(P_{3}\)-designs into bowtie and almost bowtie systems. (English) Zbl 1191.05024

Summary: This paper determines for each admissible \(w\), the set of all \(n\) such that every \(P_{3}\)-design of order \(w\) can be embedded in an (almost) bowtie system of order \(n\).

MSC:

05B07 Triple systems
05C51 Graph designs and isomorphic decomposition
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References:

[1] P. Bowling, The bowtie algorithm for Steiner triple system, Ph.D. Thesis, Auburn University, 1997; P. Bowling, The bowtie algorithm for Steiner triple system, Ph.D. Thesis, Auburn University, 1997
[2] Colbourn, C. J.; Ling, A. C.H.; Quattrocchi, G., Minimum embedding of \(P_3\)-designs into \((K_4 - e)\)-designs, J. Comb. Des., 11, 352-366 (2003) · Zbl 1028.05011
[3] Colbourn, C. J.; Ling, A. C.H.; Quattrocchi, G., Embedding path designs into kite systems, Discrete Math., 297, 38-48 (2005) · Zbl 1082.05013
[4] Gionfriddo, M.; Quattrocchi, G., Embedding balanced \(P_3\)-designs into (balanced) \(P_4\)-designs, Discrete Math., 308, 2-3, 155-160 (2008) · Zbl 1137.05012
[5] Hall, P., On representatives of subsets, J. London Math. Soc., 10, 26-32 (1935) · Zbl 0010.34503
[6] Horák, P.; Rosa, A., Decomposing Steiner triple systems into small configurations, Ars Combin., 26, 91-105 (1988) · Zbl 0780.05008
[7] Kirkman, T. P., On a problem in combinations, Cambridge and Dublin Math. J., 2, 191-204 (1847)
[8] Quattrocchi, G., Embedding path designs in 4-cycle systems, Discrete Math., 255, 349-356 (2002) · Zbl 1007.05035
[9] Sauer, N.; Schönheim, J., Maximal subsets of a given set having no triple in common with a Steiner triple system on the set, Canad, Math. Bull., 12, 777-778 (1969) · Zbl 0194.01002
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