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Colourings of path systems. (English) Zbl 07921195

Colbourn, Charles J. (ed.) et al., New advances in designs, codes and cryptography, Stinson66, Toronto, Canada, June 13–17, 2022. Cham: Springer. Fields Inst. Commun. 86, 97-123 (2024).
For the entire collection see [Zbl 1537.05001].

MSC:

05C15 Coloring of graphs and hypergraphs
05C07 Vertex degrees

References:

[1] Alspach, B., Heinrich, K., Mohar, B.: A note on Hamilton cycles in block-intersection graphs. In: Finite geometries and combinatorial designs (Lincoln, NE, 1987), Contemporary Mathematics, vol. 111, pp. 1-4. American Mathematical Society, Providence, RI (1990) · Zbl 0707.05039
[2] de Brandes, M.; Phelps, KT; Rödl, V., Coloring Steiner triple systems, SIAM J. Algebr. Discrete Methods, 3, 2, 241-249, 1982 · Zbl 0501.05036 · doi:10.1137/0603023
[3] Burgess, AC; Pike, DA, Colouring even cycle systems, Discrete Math., 308, 5-6, 962-973, 2008 · Zbl 1137.05027 · doi:10.1016/j.disc.2007.07.115
[4] Darijani, I.; Pike, DA, Colourings of star systems, J. Combin. Des., 28, 7, 525-547, 2020 · Zbl 1536.05110 · doi:10.1002/jcd.21712
[5] Forbes, AD, Uniquely 3-colourable Steiner triple systems, J. Combin. Theory Ser. A, 101, 1, 49-68, 2003 · Zbl 1012.05030 · doi:10.1016/S0097-3165(02)00016-X
[6] Hanani, H., Balanced incomplete block designs and related designs, Discrete Math., 11, 255-369, 1975 · Zbl 0361.62067 · doi:10.1016/0012-365X(75)90040-0
[7] Horák, P.; Rosa, A., Decomposing Steiner triple systems into small configurations, Ars Combin., 26, 91-105, 1988 · Zbl 0780.05008
[8] Horsley, D.; Pike, DA, On cycle systems with specified weak chromatic number, J. Combin. Theory Ser. A, 117, 8, 1195-1206, 2010 · Zbl 1206.05057 · doi:10.1016/j.jcta.2009.11.008
[9] Horsley, D.; Pike, DA, On balanced incomplete block designs with specified weak chromatic number, J. Combin. Theory Ser. A, 123, 123-153, 2014 · Zbl 1281.05021 · doi:10.1016/j.jcta.2013.12.004
[10] Lucas, É.: Les jeux de demoiselles. In: Récréations Mathématiques, vol. II, pp. 161-197. Gauthier-Villars et Fils, Paris (1892)
[11] Tarsi, M., Decomposition of a complete multigraph into simple paths: nonbalanced handcuffed designs, J. Combin. Theory Ser. A, 34, 1, 60-70, 1983 · Zbl 0511.05024 · doi:10.1016/0097-3165(83)90040-7
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