The Doyen-Wilson theorem for 3-sun systems - Lo Faro, Giovanni (Ars mathematica contemporanea, 2019)
A solution to the existence problem of $G$-designs with given subdesigns is known when ?$G$? is a triangle with ?$p = 0, 1$?, or ?$2$? disjoint pendent edges: for ?$p = 0$?, it is due to J. Doyen and R. M. Wilson Discrete Math. 5, 229-239 (1973), the first to pose such a problem for Steiner triple systems; for ?$p = 1$? and ?$p = 2$?, the corresponding designs are kite systems and bull designs, respectively. Here, a complete solution to the problem is given in the remaining case where ?$G$? is a 3-sun, i.e. a graph on six vertices consisting of a triangle with three pendent edges which form a 1-factor.
Keywords: 3-sončni sistemi; 3-sun system; diferenčna množica; difference set; embedding; oriented hypergraphs; orientirani hipergrafi; vložitev