340 KB39 KB200820252019Lo Faro, GiovanniTripodi, Antoinetteštevilka:1letnik:16str. 119-139ISSN:1855-3966COBISSID_HOST:18703449URN:URN:NBN:SI:doc-NZVQYPL0enUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporanea3-sončni sistemi3-sun systemdiferenčna množicadifference setembeddingoriented hypergraphsorientirani hipergrafivložitevThe Doyen-Wilson theorem for 3-sun systems|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-factorRešitev eksistenčnega problema ?$G$?-načrtov z danimi podnačrti je znana za primer, ko je ?$G$? trikotnik s ?$p = 0, 1$?, ali ?$2$? disjunktnimi nanj obešenimi povezavami: za ?$p = 0$? sta rešitev podala Doyen in Wilson, ki sta prva zastavila takšen problem za Steinerjeve sisteme trojic; za ?$p = 1$? so ustrezni načrti sistemi zmajev, za ?$p = 2$? pa sistemi bikov. Tukaj je dana popolna rešitev problema v preostalem primeru, ko je ?$G$? 3-sonce, tj. graf na šestih vozliščih, sestoječ iz trikotnika s tremi nanj obešenimi povezavami, ki tvorijo 1-faktorTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije