Küçükçifçi, Selda; Lindner, Curt; Quattrocchi, Gaetano Embeddings of \(P_{3}\)-designs into bowtie and almost bowtie systems. (English) Zbl 1191.05024 Discrete Math. 309, No. 18, 5675-5677 (2009). 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 \(n\). Cited in 1 Document MSC: 05B07 Triple systems 05C51 Graph designs and isomorphic decomposition Keywords:\(P_{3}\)-designs; bowtie systems; almost bowtie systems; embeddings PDFBibTeX XMLCite \textit{S. Küçükçifçi} et al., Discrete Math. 309, No. 18, 5675--5677 (2009; Zbl 1191.05024) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.