Griggs, Terry; Lo Faro, Giovanni; Quattrocchi, Gaetano On some colouring of 4-cycle systems with specified block colour patterns. (English) Zbl 1130.05008 Discrete Math. 308, No. 2-3, 465-478 (2008). Summary: The present paper continues the study (begun by G. Quattrocchi [Electron. J. Comb. 8, Paper R24 (2001; Zbl 0965.05020)] of 4-cycle systems with specified block colour patterns that are also strict colourings in the sense of V. T. Voloshin [Coloring mixed hypergraphs: theory, algorithms and applications (American Mathematical Society, Providence RI) (2002; Zbl 1001.05003)]. Here we consider colourings with patterns of size 3 or 4 such that each colour class \(C\) induces a \(P_{2}\)-design embedded into the 4-cycle system. Cited in 2 Documents MSC: 05B05 Combinatorial aspects of block designs Keywords:embedding; \(m\)-colouring; path design; 4-cycle system Citations:Zbl 0965.05020; Zbl 1001.05003 PDFBibTeX XMLCite \textit{T. Griggs} et al., Discrete Math. 308, No. 2--3, 465--478 (2008; Zbl 1130.05008) Full Text: DOI References: [1] Colbourn, C. J.; Dinitz, J. H.; Rosa, A., Bicoloring Steiner triple systems, Electron. J. Combin., 6, R25 (1999) · Zbl 0924.05007 [2] Gionfriddo, M.; Quattrocchi, G., Colouring 4-cycle systems with equitably coloured blocks, Discrete Math., 284, 137-148 (2004) · Zbl 1049.05022 [3] Milazzo, L.; Tuza, Zs., Upper chromatic number of Steiner triple and quadruple systems, Discrete Math., 174, 247-259 (1997) · Zbl 0901.05012 [4] Milazzo, L.; Tuza, Zs., Strict colourings for classes of Steiner triple systems, Discrete Math., 182, 233-243 (1998) · Zbl 0901.05013 [5] Milici, S.; Rosa, A.; Voloshin, V., Colouring Steiner systems with specified block colour patterns, Discrete Math., 240, 145-260 (2001) · Zbl 0983.05015 [6] Quattrocchi, G., Embedding path designs in 4-cycle systems, Discrete Math., 255, 349-356 (2002) · Zbl 1007.05035 [7] Quattrocchi, G., Colouring 4-cycle systems with specified block colour pattern: the case of embedding designs, Electron. J. Combin., 8, R24 (2001) · Zbl 0965.05020 [8] Voloshin, V., On the upper chromatic number of a hypergraph, Australas. J. Combin., 11, 25-45 (1995) · Zbl 0827.05027 [9] Voloshin, V., Coloring Mixed Hypergraphs: Theory, Algorithms and Applications (2002), American Mathematical Society: American Mathematical Society Providence, RI · Zbl 1001.05003 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.